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Journal articles on the topic '5d SCFT'

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Published: 1 April 2023

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1

Hwang, Chiung, Joonho Kim, Seok Kim, and Jaemo Park. "Addendum to: General instanton counting and 5d SCFT." Journal of High Energy Physics 2016, no. 4 (April 2016): 1. http://dx.doi.org/10.1007/jhep04(2016)094.

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2

Assel, Benjamin, John Estes, and Masahito Yamazaki. "Wilson Loops in 5d $${\mathcal{N} = 1}$$ SCFTs and AdS/CFT." Annales Henri Poincaré 15, no. 3 (April 21, 2013): 589–632. http://dx.doi.org/10.1007/s00023-013-0249-5.

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3

Closset, Cyril, and Michele Del Zotto. "On 5D SCFTs and their BPS quivers. Part I: B-branes and brane tilings." Advances in Theoretical and Mathematical Physics 26, no. 1 (2022): 37–142. http://dx.doi.org/10.4310/atmp.2022.v26.n1.a2.

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4

Tian, Jiahua, and Yinan Wang. "5D and 6D SCFTs from $\mathbb{C}^3$ orbifolds." SciPost Physics 12, no. 4 (April 12, 2022). http://dx.doi.org/10.21468/scipostphys.12.4.127.

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We study the orbifold singularities X=\mathbb{C}^3/\GammaX=ℂ3/Γ where \GammaΓ is a finite subgroup of SU(3)SU(3). M-theory on this orbifold singularity gives rise to a 5d SCFT, which is investigated with two methods. The first approach is via 3d McKay correspondence which relates the group theoretic data of \GammaΓ to the physical properties of the 5d SCFT. In particular, the 1-form symmetry of the 5d SCFT is read off from the McKay quiver of \GammaΓ in an elegant way. The second method is to explicitly resolve the singularity XX and study the Coulomb branch information of the 5d SCFT, which is applied to toric, non-toric hypersurface and complete intersection cases. Many new theories are constructed, either with or without an IR quiver gauge theory description. We find that many resolved Calabi-Yau threefolds, \widetilde{X}X̃, contain compact exceptional divisors that are singular by themselves. Moreover, for certain cases of \GammaΓ, the orbifold singularity \mathbb{C}^3/\Gammaℂ3/Γ can be embedded in an elliptic model and gives rise to a 6d (1,0) SCFT in the F-theory construction. Such 6d theory is naturally related to the 5d SCFT defined on the same singularity. We find examples of rank-1 6d SCFTs without a gauge group, which are potentially different from the rank-1 E-string theory.

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5

Bhardwaj, Lakshya. "Flavor symmetry of 5d SCFTs. Part II. Applications." Journal of High Energy Physics 2021, no. 4 (April 2021). http://dx.doi.org/10.1007/jhep04(2021)221.

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Abstract In Part I of this series of papers, we described a general method for determining the flavor symmetry of any 5d SCFT which can be constructed by integrating out BPS particles from some 6d SCFT compactified on a circle. In this part, we apply the method to explicitly determine the flavor symmetry of those 5d SCFTs which reduce, upon a mass deformation, to some 5d$$ \mathcal{N} $$ N = 1 gauge theory carrying a simple gauge algebra. In these cases, the flavor symmetry of the 5d gauge theory is often enhanced at the conformal point. We use our method to determine this enhancement.

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6

Apruzzi, Fabio, Sakura Schafer-Nameki, Lakshya Bhardwaj, and Jihwan Oh. "The Global Form of Flavor Symmetries and 2-Group Symmetries in 5d SCFTs." SciPost Physics 13, no. 2 (August 17, 2022). http://dx.doi.org/10.21468/scipostphys.13.2.024.

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2-group symmetries arise when 1-form symmetries and 0-form symmetries of a theory mix with each other under group multiplication. We discover the existence of 2-group symmetries in 5d \mathcal{N}=1𝒩=1 abelian gauge theories arising on the (non-extended) Coulomb branch of 5d superconformal field theories (SCFTs), leading us to argue that the UV 5d SCFT itself admits a 2-group symmetry. Furthermore, our analysis determines the global forms of the 0-form flavor symmetry groups of 5d SCFTs, irrespective of whether or not the 5d SCFT admits a 1-form symmetry. As a concrete application of our method, we analyze 2-group symmetries of all 5d SCFTs, which reduce in the IR, after performing mass deformations, to 5d \mathcal{N}=1𝒩=1 non-abelian gauge theories with simple, simply connected gauge groups. For rank-1 Seiberg theories, we check that our predictions for the flavor symmetry groups match with the superconformal and ray indices available in the literature. We also comment on the mixed `t Hooft anomaly between 1-form and 0-form symmetries arising in 5d \mathcal{N}=1𝒩=1 non-abelian gauge theories and its relation to the 2-groupS.

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7

Martone, Mario, and Gabi Zafrir. "On the compactification of 5d theories to 4d." Journal of High Energy Physics 2021, no. 8 (August 2021). http://dx.doi.org/10.1007/jhep08(2021)017.

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Abstract We study general properties of the mapping between 5d and 4d superconformal field theories (SCFTs) under both twisted circle compactification and tuning of local relevant deformation and CB moduli. After elucidating in generality when a 5d SCFT reduces to a 4d one, we identify nearly all $$ \mathcal{N} $$ N = 1 5d SCFT parents of rank-2 4d$$ \mathcal{N} $$ N = 2 SCFTs. We then use this result to map out the mass deformation trajectories among the rank-2 theories in 4d. This can be done by first understanding the mass deformations of the 5d$$ \mathcal{N} $$ N = 1 SCFTs and then map them to 4d. The former task can be easily achieved by exploiting the fact that the 5d parent theories can be obtained as the strong coupling limit of Lagrangian theories, and the latter by understanding the behavior under compactification. Finally we identify a set of general criteria that 4d moduli spaces of vacua have to satisfy when the corresponding SCFTs are related by mass deformations and check that all our RG-flows satisfy them. Many of the mass deformations we find are not visible from the corresponding complex integrable systems.

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8

Bhardwaj, Lakshya. "Flavor symmetry of 5d SCFTs. Part I. General setup." Journal of High Energy Physics 2021, no. 9 (September 2021). http://dx.doi.org/10.1007/jhep09(2021)186.

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Abstract A large class of 5d superconformal field theories (SCFTs) can be constructed by integrating out BPS particles from 6d SCFTs compactified on a circle. We describe a general method for extracting the flavor symmetry of any 5d SCFT lying in this class. For this purpose, we utilize the geometric engineering of 5d$$ \mathcal{N} $$ N = 1 theories in M-theory, where the flavor symmetry is encoded in a collection of non-compact surfaces.

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9

Apruzzi, Fabio, Sakura Schäfer-Nameki, and Yi-Nan Wang. "5d SCFTs from decoupling and gluing." Journal of High Energy Physics 2020, no. 8 (August 2020). http://dx.doi.org/10.1007/jhep08(2020)153.

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Abstract We systematically analyse 5d superconformal field theories (SCFTs) obtained by dimensional reduction from 6d $$ \mathcal{N} $$ N = (1, 0) SCFTs. Such theories have a realization as M-theory on a singular Calabi-Yau threefold, from which we determine the so-called combined fiber diagrams (CFD) introduced in [1–3]. The CFDs are graphs that encode the superconformal flavor symmetry, BPS states, low energy descriptions, as well as descendants upon flavor matter decoupling. To obtain a 5d SCFT from 6d, there are two approaches: the first is to consider a circle-reduction combined with mass deformations. The second is to circle-reduce and decouple an entire gauge sector from the theory. The former is applicable e.g. for very Higgsable theories, whereas the latter is required to obtain a 5d SCFT from a non-very Higgsable 6d theory. In the M-theory realization the latter case corresponds to decompactification of a set of compact surfaces in the Calabi-Yau threefold. To exemplify this we consider the 5d SCFTs that descend from non-Higgsable clusters and non-minimal conformal matter theories. Finally, inspired by the quiver structure of 6d theories, we propose a gluing construction for 5d SCFTs from building blocks and their CFDs.

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10

Sacchi, Matteo, Orr Sela, and Gabi Zafrir. "Compactifying 5d superconformal field theories to 3d." Journal of High Energy Physics 2021, no. 9 (September 2021). http://dx.doi.org/10.1007/jhep09(2021)149.

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Abstract Building on recent progress in the study of compactifications of 6d (1, 0) superconformal field theories (SCFTs) on Riemann surfaces to 4d$$ \mathcal{N} $$ N = 1 theories, we initiate a systematic study of compactifications of 5d$$ \mathcal{N} $$ N = 1 SCFTs on Riemann surfaces to 3d$$ \mathcal{N} $$ N = 2 theories. Specifically, we consider the compactification of the so-called rank 1 Seiberg $$ {E}_{N_f+1} $$ E N f + 1 SCFTs on tori and tubes with flux in their global symmetry, and put the resulting 3d theories to various consistency checks. These include matching the (usually enhanced) IR symmetry of the 3d theories with the one expected from the compactification, given by the commutant of the flux in the global symmetry of the corresponding 5d SCFT, and identifying the spectrum of operators and conformal manifolds predicted by the 5d picture. As the models we examine are in three dimensions, we encounter novel elements that are not present in compactifications to four dimensions, notably Chern-Simons terms and monopole superpotentials, that play an important role in our construction. The methods used in this paper can also be used for the compactification of any other 5d SCFT that has a deformation leading to a 5d gauge theory.

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11

Bhardwaj, Lakshya, and Gabi Zafrir. "Classification of 5d $$ \mathcal{N} $$ = 1 gauge theories." Journal of High Energy Physics 2020, no. 12 (December 2020). http://dx.doi.org/10.1007/jhep12(2020)099.

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Abstract We classify 5d$$ \mathcal{N} $$ N = 1 gauge theories carrying a simple gauge group that can arise by mass-deforming 5d SCFTs and 6d SCFTs (compactified on a circle, possibly with a twist). For theories having a 6d UV completion, we determine the tensor branch data of the 6d SCFT and capture the twist in terms of the tensor branch data. We also determine the dualities between these 5d gauge theories, thus determining the sets of gauge theories having a common UV completion.

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12

Closset, Cyril, Simone Giacomelli, Sakura Schäfer-Nameki, and Yi-Nan Wang. "5d and 4d SCFTs: canonical singularities, trinions and S-dualities." Journal of High Energy Physics 2021, no. 5 (May 2021). http://dx.doi.org/10.1007/jhep05(2021)274.

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Abstract Canonical threefold singularities in M-theory and Type IIB string theory give rise to superconformal field theories (SCFTs) in 5d and 4d, respectively. In this paper, we study canonical hypersurface singularities whose resolutions contain residual terminal singularities and/or 3-cycles. We focus on a certain class of ‘trinion’ singularities which exhibit these properties. In Type IIB, they give rise to 4d $$ \mathcal{N} $$ N = 2 SCFTs that we call $$ {D}_p^b $$ D p b (G)-trinions, which are marginal gaugings of three SCFTs with G flavor symmetry. In order to understand the 5d physics of these trinion singularities in M-theory, we reduce these 4d and 5d SCFTs to 3d $$ \mathcal{N} $$ N = 4 theories, thus determining the electric and magnetic quivers (or, more generally, quiverines). In M-theory, residual terminal singularities give rise to free sectors of massless hypermultiplets, which often are discretely gauged. These free sectors appear as ‘ugly’ components of the magnetic quiver of the 5d SCFT. The 3-cycles in the crepant resolution also give rise to free hypermultiplets, but their physics is more subtle, and their presence renders the magnetic quiver ‘bad’. We propose a way to redeem the badness of these quivers using a class $$ \mathcal{S} $$ S realization. We also discover new S-dualities between different $$ {D}_p^b $$ D p b (G)-trinions. For instance, a certain E8 gauging of the E8 Minahan-Nemeschansky theory is S-dual to an E8-shaped Lagrangian quiver SCFT.

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13

Hwang, Chiung, Joonho Kim, Seok Kim, and Jaemo Park. "General instanton counting and 5d SCFT." Journal of High Energy Physics 2015, no. 7 (July 2015). http://dx.doi.org/10.1007/jhep07(2015)063.

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14

Sacchi, Matteo, Orr Sela, and Gabi Zafrir. "On the 3d compactifications of 5d SCFTs associated with SU(N + 1) gauge theories." Journal of High Energy Physics 2022, no. 5 (May 2022). http://dx.doi.org/10.1007/jhep05(2022)053.

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Abstract We study the 3d$$ \mathcal{N} $$ N = 2 theories resulting from the compactification of a family of 5d SCFTs on a torus with flux in the global symmetry. The family of 5d SCFTs used in the analysis is the one that UV completes the 5d SU(N + 1) gauge theories with Chern-Simons level k and Nf fundamental hypermultiplets, generalizing the previous investigation of the torus compactifications of the rank 1 Seiberg $$ {E}_{N_{f+1}} $$ E N f + 1 SCFT (which is the N = 1 member of the family). This construction systematically yields three-dimensional theories presenting highly non-trivial non-perturbative phenomena such as infra-red dualities and enhanced symmetries, which we check using various methods.

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15

Oh, Jihwan. "OPE of line defects in 5d En SCFT." Journal of High Energy Physics 2022, no. 3 (March 2022). http://dx.doi.org/10.1007/jhep03(2022)178.

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Abstract 5d ray index is the 5d superconformal index in the presence of a ray-like defect. An elementary ray defect flows to a fundamental Wilson ray in IR gauge theory. In 5d $$ \mathcal{N} $$ N = 1 superconformal field theory(SCFT) with En global symmetry, we compute the ray index associated with an adjoint Wilson ray. We show that the operators that appear in the index are non-trivially charged under the center of the global symmetry En. The charge under the center being twice compared with the center charge carried by the elementary ray operator indicates a non-trivial OPE between the ray-like defects in the UV SCFT.

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16

Chang, Chi-Ming, Martin Fluder, Ying-Hsuan Lin, and Yifan Wang. "Proving the 6d Cardy formula and matching global gravitational anomalies." SciPost Physics 11, no. 2 (August 23, 2021). http://dx.doi.org/10.21468/scipostphys.11.2.036.

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A Cardy formula for 6d superconformal field theories (SCFTs) conjectured by Di Pietro and Komargodski in [1] governs the universal behavior of the supersymmetric partition function on S^1_\beta \times S^5Sβ1×S5 in the limit of small \betaβ and fixed squashing of the S^5S5. For a general 6d SCFT, we study its 5d effective action, which is dominated by the supersymmetric completions of perturbatively gauge-invariant Chern-Simons terms in the small \betaβ limit. Explicitly evaluating these supersymmetric completions gives the precise squashing dependence in the Cardy formula. For SCFTs with a pure Higgs branch (also known as very Higgsable SCFTs), we determine the Chern-Simons levels by explicitly going onto the Higgs branch and integrating out the Kaluza-Klein modes of the 6d fields on S^1_\betaSβ1. We then discuss tensor branch flows, where an apparent mismatch between the formula in [1] and the free field answer requires an additional contribution from BPS strings. This ``missing contribution’’ is further sharpened by the relation between the fractional part of the Chern-Simons levels and the (mixed) global gravitational anomalies of the 6d SCFT. We also comment on the Cardy formula for 4d \mathcal{N}=2𝒩=2 SCFTs in relation to Higgs branch and Coulomb branch flows.

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17

Alday, Luis F., Connor Behan, Pietro Ferrero, and Xinan Zhou. "Gluon scattering in AdS from CFT." Journal of High Energy Physics 2021, no. 6 (June 2021). http://dx.doi.org/10.1007/jhep06(2021)020.

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Abstract We present a systematic study of holographic correlators in a vast array of SCFTs with non-maximal superconformal symmetry. These theories include 4d $$ \mathcal{N} $$ N = 2 SCFTs from D3-branes near F-theory singularities, 5d Seiberg exceptional theories and 6d E-string theory, as well as 3d and 4d phenomenological models with probe flavor branes. We consider current multiplets and their generalizations with higher weights, dual to massless and massive super gluons in the bulk. At leading order in the inverse central charge expansion, connected four-point functions of these operators correspond to tree-level gluon scattering amplitudes in AdS. We show that all such tree-level four-point amplitudes in all these theories are fully fixed by symmetries and consistency conditions and explicitly construct them. Our results encode a wealth of SCFT data and exhibit various interesting emergent structures. These include Parisi-Sourlas-like dimensional reductions, hidden conformal symmetry and an AdS version of the color-kinematic duality.

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18

Bobev, Nikolay, Kiril Hristov, and Valentin Reys. "AdS5 holography and higher-derivative supergravity." Journal of High Energy Physics 2022, no. 4 (April 2022). http://dx.doi.org/10.1007/jhep04(2022)088.

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Abstract We study four-derivative corrections to 5d $$ \mathcal{N} $$ N = 2 minimal gauged supergravity using tools from conformal supergravity. There are two supersymmetric invariants at the four-derivative order and we show explicitly how to write down the action in the Poincaré frame in terms of their coefficients. We apply our results in the context of holography where the four-derivative terms in the supergravity action translate into corrections to the conformal anomalies of the dual 4d $$ \mathcal{N} $$ N = 1 SCFT. We use these results to study corrections to the entropy of the supersymmetric black string solutions of minimal supergravity. We also discuss explicit embeddings of the 5d supergravity in string and M-theory and use them to fix the higher-derivative coefficients in terms of the microscopic parameters.

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19

Closset, Cyril, Michele Del Zotto, and Vivek Saxena. "Five-dimensional SCFTs and gauge theory phases: an M-theory/type IIA perspective." SciPost Physics 6, no. 5 (May 1, 2019). http://dx.doi.org/10.21468/scipostphys.6.5.052.

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We revisit the correspondence between Calabi-Yau (CY) threefold isolated singularities \mathbf{X}𝐗 and five-dimensional superconformal field theories (SCFTs), which arise at low energy in M-theory on the space-time transverse to \mathbf{X}𝐗. Focussing on the case of toric CY singularities, we analyze the “gauge-theory phases” of the SCFT by exploiting fiberwise M-theory/type IIA duality. In this setup, the low-energy gauge group simply arises on stacks of coincident D6-branes wrapping 2-cycles in some ALE space of type A_{M-1}AM−1 fibered over a real line, and the map between the Kähler parameters of \mathbf{X}𝐗 and the Coulomb branch parameters of the field theory (masses and VEVs) can be read off systematically. Different type IIA “reductions” give rise to different gauge theory phases, whose existence depends on the particular (partial) resolutions of the isolated singularity \mathbf{X}𝐗. We also comment on the case of non-isolated toric singularities. Incidentally, we propose a slightly modified expression for the Coulomb-branch prepotential of 5d \mathcal{N}=1𝒩=1 gauge theories.

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20

Akhond, Mohammad, Federico Carta, Siddharth Dwivedi, Hirotaka Hayashi, Sung-Soo Kim, and Futoshi Yagi. "Exploring the orthosymplectic zoo." Journal of High Energy Physics 2022, no. 5 (May 2022). http://dx.doi.org/10.1007/jhep05(2022)054.

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Abstract We study the Higgs branch of the SCFT limit of 5d SO(6) and SO(8) gauge theory with hypermultiplets in the spinor and vector representations. In the case of SO(6) gauge theories, we contrast the magnetic quivers obtained with those of SU(4) gauge theory with hypermultiplets in the fundamental and second rank antisymmetric representations. Since SU(4) gauge theories admit several different values of the Chern-Simons level, we make some observations about how to distinguish those theories from the brane webs of the SO(6) theories. In the case of SO(8) gauge theories, we use SO(8) triality to propose (naively) inequivalent magnetic quivers, which will turn out to have the same moduli spaces of vacua, at least locally around their most singular loci. We encounter several interesting new phenomena occurring in the magnetic quivers, such as hypermultiplets between neighbouring symplectic gauge nodes and matter in two-index representations of unitary nodes. We also give a prescription for computing the local Coulomb branch Hilbert series for quivers involving bad USp(2) gauge nodes.

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21

Closset, Cyril, and Horia Magureanu. "The $U$-plane of rank-one 4d $\mathcal{N}=2$ KK theories." SciPost Physics 12, no. 2 (February 17, 2022). http://dx.doi.org/10.21468/scipostphys.12.2.065.

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The simplest non-trivial 5d superconformal field theories (SCFT) are the famous rank-one theories with E_nEn flavour symmetry. We study their UU-plane, which is the one-dimensional Coulomb branch of the theory on \mathbb{R}^4 \times S^1ℝ4×S1. The total space of the Seiberg-Witten (SW) geometry – the E_nEn SW curve fibered over the UU-plane – is described as a rational elliptic surface with a singular fiber of type I_{9-n}I9−n at infinity. A classification of all possible Coulomb branch configurations, for the E_nEn theories and their 4d descendants, is given by Persson’s classification of rational elliptic surfaces. We show that the global form of the flavour symmetry group is encoded in the Mordell-Weil group of the SW elliptic fibration. We study in detail many special points in parameters space, such as points where the flavour symmetry enhances, and/or where Argyres-Douglas and Minahan-Nemeschansky theories appear. In a number of important instances, including in the massless limit, the UU-plane is a modular curve, and we use modularity to investigate aspects of the low-energy physics, such as the spectrum of light particles at strong coupling and the associated BPS quivers. We also study the gravitational couplings on the UU-plane, matching the infrared expectation for the couplings A(U)A(U) and B(U)B(U) to the UV computation using the Nekrasov partition function.

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22

Bhardwaj, Lakshya. "Do all 5d SCFTs descend from 6d SCFTs?" Journal of High Energy Physics 2021, no. 4 (April 2021). http://dx.doi.org/10.1007/jhep04(2021)085.

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Abstract We present examples of 5d SCFTs that serve as counter-examples to a recently actively studied conjecture according to which it should be possible to obtain all 5d SCFTs by integrating out BPS particles from 6d SCFTs compactified on a circle. We further observe that it is possible to obtain these 5d SCFTs from 6d SCFTs if one allows integrating out BPS strings as well. Based on this observation, we propose a revised version of the conjecture according to which it should be possible to obtain all 5d SCFTs by integrating out both BPS particles and BPS strings from 6d SCFTs compactified on a circle. We describe a general procedure to integrate out BPS strings from a 5d theory once a geometric description of the 5d theory is given. We also discuss the consequences of the revised conjecture for the classification program of 5d SCFTs.

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Bhardwaj, Lakshya. "On the classification of 5d SCFTs." Journal of High Energy Physics 2020, no. 9 (September 2020). http://dx.doi.org/10.1007/jhep09(2020)007.

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Abstract We determine all 5d SCFTs upto rank three by studying RG flows of 5d KK theories. Our analysis reveals the existence of new rank one and rank two 5d SCFTs not captured by previous classifications. In addition to that, we provide for the first time a systematic and conjecturally complete classification of rank three 5d SCFTs. Our methods are based on a recently studied geometric description of 5d KK theories, thus demonstrating the utility of these geometric descriptions. It is straightforward, though computationally intensive, to extend this work and systematically classify 5d SCFTs of higher ranks (greater than or equal to four) by using the geometric description of 5d KK theories.

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Bhardwaj, Lakshya, and Patrick Jefferson. "Classifying 5d SCFTs via 6d SCFTs: arbitrary rank." Journal of High Energy Physics 2019, no. 10 (October 2019). http://dx.doi.org/10.1007/jhep10(2019)282.

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Bhardwaj, Lakshya, and Patrick Jefferson. "Classifying 5d SCFTs via 6d SCFTs: rank one." Journal of High Energy Physics 2019, no. 7 (July 2019). http://dx.doi.org/10.1007/jhep07(2019)178.

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Kim, Hee-Cheol, Sung-Soo Kim, and Kimyeong Lee. "S-foldings of 5d SCFTs." Journal of High Energy Physics 2022, no. 5 (May 2022). http://dx.doi.org/10.1007/jhep05(2022)178.

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Abstract We explore the ℤ2,3,4,6 S-foldings of some 5d superconformal field theories from the (p, q) 5-brane web perspective. The S-folding involves both a spatial quotient and an SL(2, ℤ) transformation on 5-branes simultaneously. The ℤ2,3,4,6 S-foldings are achieved by the insertion of the D4, E6, E7, E8 7-branes, respectively. The deficit angles and monodromies of these 7-branes are exactly those necessary for the S-foldings. We explore the details of the S-folding process, especially the enhancement of global flavor symmetry in various simple cases. The characteristic of the S-folding depends sharply on whether the fixed point of the discrete symmetry is at the center of a compact face (or surface), at a 5-brane, or at a crossing point of 5 branes. The analysis of the prepotential greatly supports this view of the discrete gauging.

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Bhardwaj, Lakshya, Patrick Jefferson, Hee-Cheol Kim, Houri-Christina Tarazi, and Cumrun Vafa. "Twisted circle compactifications of 6d SCFTs." Journal of High Energy Physics 2020, no. 12 (December 2020). http://dx.doi.org/10.1007/jhep12(2020)151.

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Abstract We study 6d superconformal field theories (SCFTs) compactified on a circle with arbitrary twists. The theories obtained after compactification, often referred to as 5d Kaluza-Klein (KK) theories, can be viewed as starting points for RG flows to 5d SCFTs. According to a conjecture, all 5d SCFTs can be obtained in this fashion. We compute the Coulomb branch prepotential for all 5d KK theories obtainable in this manner and associate to these theories a smooth local genus one fibered Calabi-Yau threefold in which is encoded information about all possible RG flows to 5d SCFTs. These Calabi-Yau threefolds provide hitherto unknown M-theory duals of F-theory configurations compactified on a circle with twists. For certain exceptional KK theories that do not admit a standard geometric description we propose an algebraic description that appears to retain the properties of the local Calabi-Yau threefolds necessary to determine RG flows to 5d SCFTs, along with other relevant physical data.

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28

van Beest, Marieke, Antoine Bourget, Julius Eckhard, and Sakura Schäfer-Nameki. "(5d RG-flow) trees in the tropical rain forest." Journal of High Energy Physics 2021, no. 3 (March 2021). http://dx.doi.org/10.1007/jhep03(2021)241.

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Abstract 5d superconformal field theories (SCFTs) can be obtained from 6d SCFTs by circle compactification and mass deformation. Successive decoupling of hypermultiplet matter and RG-flow generates a decoupling tree of descendant 5d SCFTs. In this paper we determine the magnetic quivers and Hasse diagrams, that encode the Higgs branches of 5d SCFTs, for entire decoupling trees. Central to this undertaking is the approach in [1], which, starting from the generalized toric polygons (GTPs) dual to 5-brane webs/tropical curves, provides a systematic and succinct derivation of magnetic quivers and their Hasse diagrams. The decoupling in the GTP description is straightforward, and generalizes the standard flop transitions of curves in toric polygons. We apply this approach to a large class of 5d KK-theories, and compute the Higgs branches for their descendants. In particular we determine the decoupling tree for all rank 2 5d SCFTs. For each tree, we also identify the flavor symmetry algebras from the magnetic quivers, including non-simply-laced flavor symmetries.

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29

Bhardwaj, Lakshya. "More 5d KK theories." Journal of High Energy Physics 2021, no. 3 (March 2021). http://dx.doi.org/10.1007/jhep03(2021)054.

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30

Gutperle, Michael, and Christoph F. Uhlemann. "Surface defects in holographic 5d SCFTs." Journal of High Energy Physics 2021, no. 4 (April 2021). http://dx.doi.org/10.1007/jhep04(2021)134.

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Abstract We use holography to study codimension-2 surface defects in 5d SCFTs engineered by (p, q) 5-brane webs. The three-dimensional defects are realized by D3-branes ending on the brane web. We identify the holographic representation of the defects in Type IIB AdS6 solutions as probe D3-branes, and study conformal and non-conformal defects which, respectively, preserve one half and one quarter of the supersymmetry. For a sample of 5d SCFTs, including the TN theories, we provide explicit solutions for conformal and non-conformal defects. For the conformal defects we obtain their contribution to the free energy on S5.

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31

Del Zotto, Michele, Jonathan J. Heckman, Shani Nadir Meynet, Robert Moscrop, and Hao Y. Zhang. "Higher symmetries of 5D orbifold SCFTs." Physical Review D 106, no. 4 (August 24, 2022). http://dx.doi.org/10.1103/physrevd.106.046010.

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32

Jefferson, Patrick, Sheldon Katz, Hee-Cheol Kim, and Cumrun Vafa. "On geometric classification of 5d SCFTs." Journal of High Energy Physics 2018, no. 4 (April 2018). http://dx.doi.org/10.1007/jhep04(2018)103.

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33

Bhardwaj, Lakshya, and Patrick Jefferson. "Addendum to: Classifying 5d SCFTs via 6d SCFTs: rank one." Journal of High Energy Physics 2020, no. 1 (January 2020). http://dx.doi.org/10.1007/jhep01(2020)153.

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34

Sabag, Evyatar, and Matteo Sacchi. "A 5d perspective on the compactifications of 6d SCFTs to 4d $$ \mathcal{N} $$ = 1 SCFTs." Journal of High Energy Physics 2022, no. 12 (December 5, 2022). http://dx.doi.org/10.1007/jhep12(2022)017.

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Abstract Compactifying 6d superconformal field theories (SCFTs) to 4d $$ \mathcal{N} $$ N = 1 theories on two-punctured spheres (tubes) and tori with flux is realized using duality domain walls in 5d $$ \mathcal{N} $$ N = 1 Kaluza-Klein (KK) theories, which are usually denoted by flux domain walls. We revisit this construction and study it in detail from the 5d perspective, specifically rephrasing it using the box graph description of the extended Coulomb branch phases of 5d theories. This perspective could be helpful in understanding how to equivalently realize the 4d $$ \mathcal{N} $$ N = 1 models from geometric engineering in M-theory. Along the way, we show how to recover various properties of the 4d theories from the 5d perspective, such as the flux associated to the domain wall configurations and the presence of a $$ \mathfrak{u} $$ u (1) global symmetry in the 4d theory descending from the KK symmetry on the tube, which is broken to a discrete subgroup on a flux torus. We demonstrate all of these ideas using the rank 1 E-string theory.

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35

Hübner, Max. "5d SCFTs from (En, Em) conformal matter." Journal of High Energy Physics 2020, no. 12 (December 2020). http://dx.doi.org/10.1007/jhep12(2020)014.

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Abstract We determine 5d $$ \mathcal{N} $$ N = 1 SCFTs originating from 6d (En, Em) conformal matter theories with n ≠ m by circle reduction and mass deformations. The marginal geometries are constructed and we derive their combined fiber diagrams (CFDs). The CFDs allow for an enumeration of descendant SCFTs obtained by decoupling matter hypermultiplets and a description of candidate weakly coupled quivers.

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36

Kim, Hee-Cheol, Minsung Kim, Sung-Soo Kim, and Ki-Hong Lee. "Bootstrapping BPS spectra of 5d/6d field theories." Journal of High Energy Physics 2021, no. 4 (April 2021). http://dx.doi.org/10.1007/jhep04(2021)161.

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Abstract We propose a systematic approach to computing the BPS spectrum of any 5d/6d supersymmetric quantum field theory in Coulomb phases, which admits either gauge theory descriptions or geometric descriptions, based on the Nakajima-Yoshioka’s blowup equations. We provide a significant generalization of the blowup equation approach in terms of both properly quantized magnetic fluxes on the blowup $$ \hat{\mathrm{\mathbb{C}}} $$ ℂ ̂ 2 and the effective prepotential for 5d/6d field theories on the Omega background which is uniquely determined by the Chern-Simons couplings on their Coulomb branches. We employ our method to compute BPS spectra of all rank-1 and rank-2 5d Kaluza-Klein (KK) theories descending from 6d $$ \mathcal{N} $$ N = (1, 0) superconformal field theories (SCFTs) compactified on a circle with/without twist. We also discuss various 5d SCFTs and KK theories of higher ranks, which include a few exotic cases such as new rank-1 and rank-2 5d SCFTs engineered with frozen singularity as well as the 5d SU(3)8 gauge theory currently having neither a brane web nor a smooth shrinkable geometric description. The results serve as non-trivial checks for a large class of non-trivial dualities among 5d theories and also as independent evidences for the existence of certain exotic theories.

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37

Closset, Cyril, Sakura Schäfer-Nameki, and Yi-Nan Wang. "Coulomb and Higgs branches from canonical singularities. Part I. Hypersurfaces with smooth Calabi-Yau resolutions." Journal of High Energy Physics 2022, no. 4 (April 2022). http://dx.doi.org/10.1007/jhep04(2022)061.

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Abstract Compactification of M-theory and of IIB string theory on threefold canonical singularities gives rise to superconformal field theories (SCFTs) in 5d and 4d, respectively. The resolutions and deformations of the singularities encode salient features of the SCFTs and of their moduli spaces. In this paper, we build on Part 0 of this series [1] and further explore the physics of SCFTs arising from isolated hypersurface singularities. We study in detail these canonical isolated hypersurface singularities that admit a smooth Calabi-Yau (crepant) resolution. Their 5d and 4d physics is discussed and their 3d reduction and mirrors (the magnetic quivers) are determined in many cases. As an explorative tool, we provide a Mathematica code which computes key quantities for any canonical isolated hypersurface singularity, including the 5d rank, the 4d Coulomb branch spectrum and central charges, higher-form symmetries in 4d and 5d, and crepant resolutions.

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38

Roychowdhury, Dibakar. "Nonintegrability for N=1 SCFTs in 5D." Physical Review D 104, no. 8 (October 4, 2021). http://dx.doi.org/10.1103/physrevd.104.086010.

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39

Del Zotto, Michele, Jonathan J. Heckman, and David R. Morrison. "6D SCFTs and phases of 5D theories." Journal of High Energy Physics 2017, no. 9 (September 2017). http://dx.doi.org/10.1007/jhep09(2017)147.

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40

Hayashi, Hirotaka, Sung-Soo Kim, Kimyeong Lee, Masato Taki, and Futoshi Yagi. "More on 5d descriptions of 6d SCFTs." Journal of High Energy Physics 2016, no. 10 (October 2016). http://dx.doi.org/10.1007/jhep10(2016)126.

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41

Zafrir, Gabi. "Compactifications of 5d SCFTs with a twist." Journal of High Energy Physics 2017, no. 1 (January 2017). http://dx.doi.org/10.1007/jhep01(2017)097.

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42

Gutperle, Michael, Justin Kaidi, and Himanshu Raj. "Mass deformations of 5d SCFTs via holography." Journal of High Energy Physics 2018, no. 2 (February 2018). http://dx.doi.org/10.1007/jhep02(2018)165.

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43

Fluder, Martin, and Christoph F. Uhlemann. "Evidence for a 5d F-theorem." Journal of High Energy Physics 2021, no. 2 (February 2021). http://dx.doi.org/10.1007/jhep02(2021)192.

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Abstract Renormalization group flows are studied between 5d SCFTs engineered by (p, q) 5-brane webs with large numbers of external 5-branes. A general expression for the free energy on S5 in terms of single-valued trilogarithm functions is derived from their supergravity duals, which are characterized by the 5-brane charges and additional geometric parameters. The additional geometric parameters are fixed by regularity conditions, and we show that the solutions to the regularity conditions extremize a trial free energy. These results are used to survey a large sample of $$ \mathcal{O} $$ O (105) renormalization group flows between different 5d SCFTs, including Higgs branch flows and flows that preserve the SU(2) R- symmetry. In all cases the free energy changes monotonically towards the infrared, in line with a 5d F -theorem.

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44

Closset, Cyril, Sakura Schäfer-Nameki, and Yi-Nan Wang. "Coulomb and Higgs branches from canonical singularities. Part 0." Journal of High Energy Physics 2021, no. 2 (February 2021). http://dx.doi.org/10.1007/jhep02(2021)003.

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Abstract Five- and four-dimensional superconformal field theories with eight supercharges arise from canonical threefold singularities in M-theory and Type IIB string theory, respectively. We study their Coulomb and Higgs branches using crepant resolutions and deformations of the singularities. We propose a relation between the resulting moduli spaces, by compactifying the theories to 3d, followed by 3d $$ \mathcal{N} $$ N = 4 mirror symmetry and an S-type gauging of an abelian flavor symmetry. In particular, we use this correspondence to determine the Higgs branch of some 5d SCFTs and their magnetic quivers from the geometry. As an application of the general framework, we observe that singularities that engineer Argyres-Douglas theories in Type IIB also give rise to rank-0 5d SCFTs in M-theory. We also compute the higher-form symmetries of the 4d and 5d SCFTs, including the one-form symmetries of generalized Argyres-Douglas theories of type (G, G′).

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45

Hayashi, Hirotaka, Sung-Soo Kim, Kimyeong Lee, and Futoshi Yagi. "6d SCFTs, 5d dualities and Tao web diagrams." Journal of High Energy Physics 2019, no. 5 (May 2019). http://dx.doi.org/10.1007/jhep05(2019)203.

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46

Chang, Chi-Ming. "5d and 6d SCFTs have no weak coupling limit." Journal of High Energy Physics 2019, no. 9 (September 2019). http://dx.doi.org/10.1007/jhep09(2019)016.

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47

Uhlemann, Christoph F. "Exact results for 5d SCFTs of long quiver type." Journal of High Energy Physics 2019, no. 11 (November 2019). http://dx.doi.org/10.1007/jhep11(2019)072.

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48

Hayashi, Hirotaka, Sung-Soo Kim, Kimyeong Lee, and Futoshi Yagi. "Dualities and 5-brane webs for 5d rank 2 SCFTs." Journal of High Energy Physics 2018, no. 12 (December 2018). http://dx.doi.org/10.1007/jhep12(2018)016.

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49

Chang, Chi-Ming, Ori J. Ganor, and Jihwan Oh. "An index for ray operators in 5d E n SCFTs." Journal of High Energy Physics 2017, no. 2 (February 2017). http://dx.doi.org/10.1007/jhep02(2017)018.

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50

Fluder, Martin, Seyed Morteza Hosseini, and Christoph F. Uhlemann. "Black hole microstate counting in Type IIB from 5d SCFTs." Journal of High Energy Physics 2019, no. 5 (May 2019). http://dx.doi.org/10.1007/jhep05(2019)134.

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