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Published: 9 March 2023
Last updated: 10 March 2023

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1

Mateos, Toni. "Marginal deformations of Script N=4 SYM and Penrose limits with continuous spectrum." Journal of High Energy Physics 2005, no. 08 (August 4, 2005): 026. http://dx.doi.org/10.1088/1126-6708/2005/08/026.

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2

LEIGH, ROBERT G. "MARGINAL DEFORMATIONS OF N=4 SYM AND NON-COMMUTATIVE MODULI SPACES OF VACUA." International Journal of Modern Physics A 16, supp01c (September 2001): 955–57. http://dx.doi.org/10.1142/s0217751x0100859x.

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We review recent work on the application of the non-commutative geometric framework to an interpretation of the moduli space of vacua of marginal deformations of N = 4 super Yang-Mills theories. At rational values of couplings, different regions of moduli space may be associated with D5-branes of various topologies, and orbifold dual descriptions exist which may be accessed by T-duality. Singularities in the moduli space are associated with topology change.
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3

Aharony, Ofer, and Shlomo S. Razamat. "Exactly Marginal Deformations of Script N = 4 SYM and of its Supersymmetric Orbifold Descendants." Journal of High Energy Physics 2002, no. 05 (May 17, 2002): 029. http://dx.doi.org/10.1088/1126-6708/2002/05/029.

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4

Aharony, Ofer, Barak Kol, and Shimon Yankielowicz. "On exactly marginal deformations of Script N = 4 SYM and Type IIB Supergravity onAdS5×S5." Journal of High Energy Physics 2002, no. 06 (June 17, 2002): 039. http://dx.doi.org/10.1088/1126-6708/2002/06/039.

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5

Kulaxizi, M., and K. Zoubos. "Marginal deformations of tree-level  = 4 SYM from twistor string theory." Fortschritte der Physik 54, no. 5-6 (May 4, 2006): 423–29. http://dx.doi.org/10.1002/prop.200510299.

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6

Ünsal, Mithat. "Supersymmetric deformations of type IIB matrix model as matrix regularization of Script N = 4 SYM." Journal of High Energy Physics 2006, no. 04 (April 3, 2006): 002. http://dx.doi.org/10.1088/1126-6708/2006/04/002.

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7

Vesman, A. V., and B. V. Ivanov. "Types of sea ice conditions north of Spitzbergen archipelago." Arctic and Antarctic Research 68, no. 2 (July 3, 2022): 118–32. http://dx.doi.org/10.30758/0555-2648-2022-68-2-118-132.

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Sea ice is an important part of the Arctic climate system. In the recent decade, rapid changes in the sea ice conditions have been observed: sea ice extent and sea ice thickness are declining; conversely, ice drift speed and deformations are increasing [1–10]. The main aim of this paper was to describe the variability of sea ice conditions north of the Svalbard archipelago and analyze the changes occurring there. For most of the year, a stable polynya is observed north of the archipelago, which is commonly called “Whalers Bay”. The prevailing wind direction (8–9 months out of 12) is north-east, thus, almost throughout the whole year, conditions persist that support the flow of warmer Atlantic waters (AW) to the surface. Stable upwelling, together with the observed increase in AW’s temperature, contributes to the formation of the quasi-stationary polynya “Whalers Bay”. The ice conditions north of the Spitsbergen archipelago are changing extremely dynamically. However, all their diversity can be grouped into four main types. Type 1 — the area to the north of the archipelago is covered with ice; type 2 — the ice edge moves to the north of the archipelago; 3 — “Whalers Bay” polynya; 4 — an intermediate type, when a “passage” is formed to the Barents Sea between the ice edge and the northern coast of the archipelago. This study showed that since the mid-1990s the frequency of type 1 has significantly decreased, conversely, type 3 has become predominant, and the frequency of occurrence of type 2 has also increased. The maximum area of the polynya was observed in February 2012 and 2014, when the ice edge reached 82,5°N and 50°E, and 83°N and 46°E respectively. The lightest ice conditions were observed in 2012, 2013 and 2016. The main periods of 2–3, 5–6 and 14 years were identified in open water area variability. The ice cover to the north of the archipelago is largely presented by the conditions similar to the marginal ice zone with an actively changing ice edge configuration and the combined influence of factors characteristic of open sea areas and ice-covered areas. It is here that intense heat exchange takes place between the ocean and the atmosphere. The heat fluxes directed from the ocean to the atmosphere in the area of the polynya have increased by about 4 TW over the past 40 years. The highest correlation between the heat flux and the area of open water is observed with a lag of 2 months.
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8

Jin, Qingjun. "Emergent supersymmetry in the marginal deformations of N = 4 $$ \mathcal{N}=4 $$ SYM." Journal of High Energy Physics 2016, no. 10 (October 2016). http://dx.doi.org/10.1007/jhep10(2016)131.

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9

Arav, Igal, Jerome P. Gauntlett, Matthew M. Roberts, and Christopher Rosen. "Marginal deformations and RG flows for type IIB S-folds." Journal of High Energy Physics 2021, no. 7 (July 2021). http://dx.doi.org/10.1007/jhep07(2021)151.

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Abstract We construct a continuous one parameter family of AdS4× S1× S5 S-fold solutions of type IIB string theory which have nontrivial SL(2, ℤ) monodromy in the S1 direction. The solutions span a subset of a conformal manifold that contains the known $$ \mathcal{N} $$ N = 4 S-fold SCFT in d = 3, and generically preserve $$ \mathcal{N} $$ N = 2 supersymmetry. We also construct RG flows across dimensions, from AdS5× S5, dual to $$ \mathcal{N} $$ N = 4, d = 4 SYM compactified with a twisted spatial circle, to various AdS4×S1×S5 S-fold solutions, dual to d = 3 SCFTs. We construct additional flows between the AdS5 dual of the Leigh-Strassler SCFT and an $$ \mathcal{N} $$ N = 2 S-fold as well as RG flows between various S-folds.
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10

Arav, Igal, K. C. Matthew Cheung, Jerome P. Gauntlett, Matthew M. Roberts, and Christopher Rosen. "Spatially modulated and supersymmetric mass deformations of $$ \mathcal{N} $$ = 4 SYM." Journal of High Energy Physics 2020, no. 11 (November 2020). http://dx.doi.org/10.1007/jhep11(2020)156.

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Abstract We study mass deformations of $$ \mathcal{N} $$ N = 4, d = 4 SYM theory that are spatially modulated in one spatial dimension and preserve some residual supersymmetry. We focus on generalisations of $$ \mathcal{N} $$ N = 1∗ theories and show that it is also possible, for suitably chosen supersymmetric masses, to preserve d = 3 conformal symmetry associated with a co-dimension one interface. Holographic solutions can be constructed using D = 5 theories of gravity that arise from consistent truncations of SO(6) gauged supergravity and hence type IIB supergravity. For the mass deformations that preserve d = 3 superconformal symmetry we construct a rich set of Janus solutions of $$ \mathcal{N} $$ N = 4 SYM theory which have the same coupling constant on either side of the interface. Limiting classes of these solutions give rise to RG interface solutions with $$ \mathcal{N} $$ N = 4 SYM on one side of the interface and the Leigh-Strassler (LS) SCFT on the other, and also to a Janus solution for the LS theory. Another limiting solution is a new supersymmetric AdS4× S1× S5 solution of type IIB supergravity.
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11

Harmark, Troels, and Matthias Wilhelm. "Solving the Hagedorn temperature of AdS5/CFT4 via the Quantum Spectral Curve: chemical potentials and deformations." Journal of High Energy Physics 2022, no. 7 (July 2022). http://dx.doi.org/10.1007/jhep07(2022)136.

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Abstract We describe how to calculate the Hagedorn temperature of $$ \mathcal{N} $$ N = 4 SYM theory and type IIB superstring theory on AdS5 × S5 via the Quantum Spectral Curve (QSC) — providing further details on our previous letters [1] and [2]. We solve the QSC equations perturbatively at weak ‘t Hooft coupling λ up to seven-loop order and numerically at finite coupling, finding that the perturbative results can be expressed in terms of single-valued harmonic polylogarithms. Moreover, we generalize the QSC to describe the Hagedorn temperature in the presence of chemical potentials. Finally, we show that the Hagedorn temperature in certain deformations of $$ \mathcal{N} $$ N = 4 SYM theory (real-β and γi deformation) agrees with the one in $$ \mathcal{N} $$ N = 4 SYM theory at any value of λ.
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12

Arav, Igal, K. C. Matthew Cheung, Jerome P. Gauntlett, Matthew M. Roberts, and Christopher Rosen. "Superconformal RG interfaces in holography." Journal of High Energy Physics 2020, no. 11 (November 2020). http://dx.doi.org/10.1007/jhep11(2020)168.

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Abstract We construct gravitational solutions that holographically describe two different d = 4 SCFTs joined together at a co-dimension one, planar RG interface and preserving d = 3 superconformal symmetry. The RG interface joins $$ \mathcal{N} $$ N = 4 SYM theory on one side with the $$ \mathcal{N} $$ N = 1 Leigh-Strassler SCFT on the other. We construct a family of such solutions, which in general are associated with spatially dependent mass deformations on the $$ \mathcal{N} $$ N = 4 SYM side, but there is a particular solution for which these deformations vanish. We also construct a Janus solution with the Leigh-Strassler SCFT on either side of the interface. Gravitational solutions associated with superconformal interfaces involving ABJM theory and two d = 3 $$ \mathcal{N} $$ N = 1 SCFTs with G2 symmetry are also discussed and shown to have similar properties, but they also exhibit some new features.
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13

Bachas, Constantin, Ioannis Lavdas, and Bruno Le Floch. "Marginal deformations of 3d $$ \mathcal{N} $$ = 4 linear quiver theories." Journal of High Energy Physics 2019, no. 10 (October 2019). http://dx.doi.org/10.1007/jhep10(2019)253.

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14

Berenstein, David, and Eric Dzienkowski. "Giant gravitons and the emergence of geometric limits in β-deformations of N = 4 $$ \mathcal{N}=4 $$ SYM." Journal of High Energy Physics 2015, no. 1 (January 2015). http://dx.doi.org/10.1007/jhep01(2015)126.

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15

Bena, Iosif, Mariana Graña, Stanislav Kuperstein, Praxitelis Ntokos, and Michela Petrini. "Fermionic and bosonic mass deformations of N $$ \mathcal{N} $$ = 4 SYM and their bulk supergravity dual." Journal of High Energy Physics 2016, no. 5 (May 2016). http://dx.doi.org/10.1007/jhep05(2016)149.

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16

Buican, Matthew, and Takahiro Nishinaka. "$$ \mathcal{N} $$ = 4 SYM, Argyres-Douglas theories, and an exact graded vector space isomorphism." Journal of High Energy Physics 2022, no. 4 (April 2022). http://dx.doi.org/10.1007/jhep04(2022)028.

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Abstract In this first of two papers, we explain in detail the simplest example of a broader set of relations between apparently very different theories. Our example relates $$ \mathfrak{su}(2) $$ su 2 $$ \mathcal{N} $$ N = 4 super Yang-Mills (SYM) to a theory we call “(3, 2)”. This latter theory is an exactly marginal diagonal SU(2) gauging of three D3(SU(2)) Argyres-Douglas (AD) theories. We begin by observing that the Schur indices of these two theories are related by an algebraic transformation that is surprisingly reminiscent of index transformations describing spontaneous symmetry breaking on the Higgs branch. However, this transformation breaks half the supersymmetry of the SYM theory as well as its full $$ \mathcal{N} $$ N = 2 SU(2)F flavor symmetry. Moreover, it does so in an interesting way when viewed through the lens of the corresponding 2D vertex operator algebras (VOAs): affine currents of the small $$ \mathcal{N} $$ N = 4 super-Virasoro algebra at c = −9 get mapped to the $$ \mathcal{A}(6) $$ A 6 stress tensor and some of its conformal descendants, while the extra supersymmetry currents on the $$ \mathcal{N} $$ N = 4 side get mapped to higher-dimensional fermionic currents and their descendants on the $$ \mathcal{A}(6) $$ A 6 side. We prove these relations are facets of an exact graded vector space isomorphism (GVSI) between these two VOAs. This GVSI respects the U(1)r charge of the parent 4D theories. We briefly sketch how more general $$ \mathfrak{su}(N) $$ su N $$ \mathcal{N} $$ N = 4 SYM theories are related to an infinite class of AD theories via generalizations of our example. We conclude by showing that, in this class of theories, the $$ \mathcal{A}(6) $$ A 6 VOA saturates a new inequality on the number of strong generators.
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17

Zacarías, Salomon. "Marginal deformations of a class of AdS3 $$ \mathcal{N} $$ = (0, 4) holographic backgrounds." Journal of High Energy Physics 2021, no. 6 (June 2021). http://dx.doi.org/10.1007/jhep06(2021)017.

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Abstract We discuss marginal deformations of warped AdS3×S2 solutions preserving small $$ \mathcal{N} $$ N = (0, 4) supersymmetry in massive IIA and eleven-dimensional supergravity and obtain a whole family of new solutions. We characterise these new backgrounds by studying some observables like the quantised charges, associated Hannany-Witten brane set-ups and the holographic central charge, the latter is shown to be invariant under the deformation. The study of the preservation of supersymmetry shows that the new backgrounds support a dynamical SU(2) structure on the internal five-dimensional space.
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18

Naseer, Usman, and Charles Thull. "Flavor deformations and supersymmetry enhancement in $4d$ $\mathcal{N}=2$ theories." SciPost Physics 13, no. 3 (September 21, 2022). http://dx.doi.org/10.21468/scipostphys.13.3.058.

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We study \mathcal{N}=2𝒩=2 theories on four-dimensional manifolds that admit a Killing vector vv with isolated fixed points. It is possible to deform these theories by coupling position-dependent background fields to the flavor current multiplet. The partition function of the deformed theory only depends on the value of the background scalar fields at the fixed points of vv. For a single adjoint hypermultiplet, the partition function becomes independent of the supergravity as well as the flavor background if the scalars attain special values at the fixed points. For these special values, supersymmetry at the fixed points enhances from the Donaldson-Witten twist to the Marcus twist or the Vafa-Witten twist of \mathcal{N}=4𝒩=4 SYM. Our results explain the recently observed squashing independence of \mathcal{N}=2^*𝒩=2* theory on the squashed sphere and provide a new squashing independent point. Interpreted through the AGT-correspondence, this implies the bb-independence of torus one-point functions of certain operators in Liouville/Toda CFT. The position-dependent deformations imply relations between correlators of partially integrated operators in \mathcal{N}=2𝒩=2 SCFT with flavor symmetries.
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19

Chicherin, Dmitry, and Gregory P. Korchemsky. "The SAGEX review on scattering amplitudes, chapter 9: integrability of amplitudes in fishnet theories." Journal of Physics A: Mathematical and Theoretical, August 24, 2022. http://dx.doi.org/10.1088/1751-8121/ac8c72.

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Abstract We discuss the properties of scattering amplitudes in a conformal bi-scalar fishnet theory that previously appeared in the study of integrable deformations of N=4 SYM. In distinction with the latter theory, the scattering amplitudes in the conformal fishnet theory do not suffer from infrared divergences and possess enhanced symmetries. We demonstrate that for the simplest four-particle scattering the single- and double-trace partial amplitudes can be computed for arbitrary coupling in the leading color approximation. We also review the invariance of single-trace components of multi-particle fishnet amplitudes in the leading color limit under infinite-dimensional Yangian symmetry.
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20

Guarino, Adolfo, and Colin Sterckx. "Flat deformations of type IIB S-folds." Journal of High Energy Physics 2021, no. 11 (November 2021). http://dx.doi.org/10.1007/jhep11(2021)171.

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Abstract Type IIB S-folds of the form AdS4× S1× S5 have been shown to contain axion-like deformations parameterising flat directions in the 4D scalar potential and corresponding to marginal deformations of the dual S-fold CFT’s. In this note we present a group-theoretical characterisation of such flat deformations and provide a 5D interpretation thereof in terms of $$ \mathfrak{s}(6) $$ s 6 -valued duality twists inducing a class of Cremmer-Scherk-Schwarz flat gaugings in a reduction from 5D to 4D. In this manner we establish the existence of two flat deformations for the $$ \mathcal{N} $$ N = 4 and SO(4) symmetric S-fold causing a symmetry breaking down to its U(1)2 Cartan subgroup. The result is a new two-parameter family of non-supersymmetric S-folds which are perturbatively stable at the lower-dimensional supergravity level, thus providing the first examples of such type IIB backgrounds.
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21

Arav, Igal, K. C. Matthew Cheung, Jerome P. Gauntlett, Matthew M. Roberts, and Christopher Rosen. "A new family of AdS4 S-folds in type IIB string theory." Journal of High Energy Physics 2021, no. 5 (May 2021). http://dx.doi.org/10.1007/jhep05(2021)222.

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Abstract We construct infinite new classes of AdS4× S1× S5 solutions of type IIB string theory which have non-trivial SL(2, ℤ) monodromy along the S1 direction. The solutions are supersymmetric and holographically dual, generically, to $$ \mathcal{N} $$ N = 1 SCFTs in d = 3. The solutions are first constructed as AdS4× ℝ solutions in D = 5 SO(6) gauged supergravity and then uplifted to D = 10. Unlike the known AdS4× ℝ S-fold solutions, there is no continuous symmetry associated with the ℝ direction. The solutions all arise as limiting cases of Janus solutions of d = 4, $$ \mathcal{N} $$ N = 4 SYM theory which are supported both by a different value of the coupling constant on either side of the interface, as well as by fermion and boson mass deformations. As special cases, the construction recovers three known S-fold constructions, preserving $$ \mathcal{N} $$ N = 1, 2 and 4 supersymmetry, as well as a recently constructed $$ \mathcal{N} $$ N = 1 AdS4× S1× S5 solution (not S-folded). We also present some novel “one-sided Janus” solutions that are non-singular.
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22

Chai, Noam, Eliezer Rabinovici, Ritam Sinha, and Michael Smolkin. "The bi-conical vector model at 1/N." Journal of High Energy Physics 2021, no. 5 (May 2021). http://dx.doi.org/10.1007/jhep05(2021)192.

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Abstract We study finite N aspects of the O(m) × O(N − m) vector model with quartic interactions in general 2 ≤ d ≤ 6 spacetime dimensions. This model has recently been shown [1, 2] to display the phenomenon of persistent symmetry breaking at a perturbative Wilson-Fisher-like fixed point in d = 4 − ϵ dimensions. The large rank limit of the biconical model displays a conformal manifold and a moduli space of vacua. We find a set of three double trace scalar operators that are respectively irrelevant, relevant and marginal deformations of the conformal manifold in general d. We calculate the anomalous dimensions of the single and multi-trace scalar operators to the first sub-leading order in the large rank expansion. The anomalous dimension of the marginal operator does not vanish in general, indicating that the conformal manifold is lifted at finite N . In the case of equal ranks we are able to derive explicitly the scaling dimensions of various operators as functions of only d.
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23

Beratto, Emanuele, Noppadol Mekareeya, and Matteo Sacchi. "Marginal operators and supersymmetry enhancement in 3d S-fold SCFTs." Journal of High Energy Physics 2020, no. 12 (December 2020). http://dx.doi.org/10.1007/jhep12(2020)017.

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Abstract The study of exactly marginal deformations of superconformal field theories is a topic that has received considerable attention due to their rich properties. We investigate the $$ \mathcal{N} $$ N = 2 preserving exactly marginal operators of 3d S-fold SCFTs. Two families of such theories are considered: one is constructed by gauging the diagonal flavour symmetry of the T(U(2)) and T(U(3)) theories, and the other by gauging the diagonal flavour symmetry of the $$ {T}_{\left[2,{1}^2\right]}^{\left[2,{1}^2\right]}\left( SU(4)\right) $$ T 2 1 2 2 1 2 SU 4 theory. In both families, it is possible to turn on a Chern-Simons level for each gauge group and to couple to each theory various numbers of hypermultiplets. The detailed analysis of the exactly marginal operators, along with the superconformal indices, allows us to determine whether supersymmetry gets enhanced in the infrared and to deduce the amount of supersymmetry of the corresponding SCFT.
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24

Niarchos, Vasilis, and Kyriakos Papadodimas. "On the Kähler-Hodge structure of superconformal manifolds." Journal of High Energy Physics 2022, no. 9 (September 14, 2022). http://dx.doi.org/10.1007/jhep09(2022)104.

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Abstract We show that conformal manifolds in d ≥ 3 conformal field theories with at least 4 supercharges are Kähler-Hodge, thus extending to 3d $$ \mathcal{N} $$ N = 2 and 4d $$ \mathcal{N} $$ N = 1 similar results previously derived for 4d $$ \mathcal{N} $$ N = 2 and $$ \mathcal{N} $$ N = 4 and various types of 2d SCFTs. Conformal manifolds in SCFTs are equipped with a holomorphic line bundle ℒ, which encodes the operator mixing of supercharges under marginal deformations. Using conformal perturbation theory and superconformal Ward identities, we compute the curvature of ℒ at a generic point on the conformal manifold. We show that the Kähler form of the Zamolodchikov metric is proportional to the first Chern class of ℒ, with a constant of proportionality given by the two-point function coefficient of the stress tensor, CT. In cases where certain additional conditions about the nature of singular points on the conformal manifold hold, this implies a quantization condition for the total volume of the conformal manifold.
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25

Eberhardt, Lorenz. "Summing over geometries in string theory." Journal of High Energy Physics 2021, no. 5 (May 2021). http://dx.doi.org/10.1007/jhep05(2021)233.

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Abstract We examine the question how string theory achieves a sum over bulk geometries with fixed asymptotic boundary conditions. We discuss this problem with the help of the tensionless string on $$ {\mathrm{\mathcal{M}}}_3\times {\mathrm{S}}^3\times {\mathbbm{T}}^4 $$ ℳ 3 × S 3 × T 4 (with one unit of NS-NS flux) that was recently understood to be dual to the symmetric orbifold SymN ($$ {\mathbbm{T}}^4 $$ T 4 ). We strengthen the analysis of [1] and show that the perturbative string partition function around a fixed bulk background already includes a sum over semi-classical geometries and large stringy corrections can be interpreted as various semi-classical geometries. We argue in particular that the string partition function on a Euclidean wormhole geometry factorizes completely into factors associated to the two boundaries of spacetime. Central to this is the remarkable property of the moduli space integral of string theory to localize on covering spaces of the conformal boundary of ℳ3. We also emphasize the fact that string perturbation theory computes the grand canonical partition function of the family of theories ⊕N SymN ($$ {\mathbbm{T}}^4 $$ T 4 ). The boundary partition function is naturally expressed as a sum over winding worldsheets, each of which we interpret as a ‘stringy geometry’. We argue that the semi-classical bulk geometry can be understood as a condensate of such stringy geometries. We also briefly discuss the effect of ensemble averaging over the Narain moduli space of $$ {\mathbbm{T}}^4 $$ T 4 and of deforming away from the orbifold by the marginal deformation.
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26

Lima, A. A., G. M. Sotkov, and M. Stanishkov. "On the dynamics of protected ramond ground states in the D1-D5 CFT." Journal of High Energy Physics 2021, no. 7 (July 2021). http://dx.doi.org/10.1007/jhep07(2021)120.

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Abstract We examine the behavior of the Ramond ground states in the D1-D5 CFT after a deformation of the free-orbifold sigma model on target space ($$ {\mathbbm{T}}^4 $$ T 4 )N/SN by a marginal interaction operator. These states are compositions of Ramond ground states of the twisted and untwisted sectors. They are characterized by a conjugacy class of SN and by the set of their “spins”, including both R-charge and “internal” SU(2) charge. We compute the four-point functions of an arbitrary Ramond ground state with its conjugate and two interaction operators, for genus-zero covering surfaces representing the leading orders in the large-N expansion. We examine short distance limits of these four-point functions, shedding light on the dynamics of the interacting theory. We find the OPEs and a collection of structure constants of the ground states with the interaction operators and a set of resulting non-BPS twisted operators. We also calculate the integrals of the four-point functions over the positions of the interaction operators and show that they vanish. This provides an explicit demonstration that the Ramond ground states remain protected against deformations away of the free orbifold point, as expected from algebraic considerations using the spectral flow of the $$ \mathcal{N} $$ N = (4, 4) superconformal algebra with central charge c = 6N.
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27

Awata, Hidetoshi, Hiroaki Kanno, Andrei Mironov, and Alexei Morozov. "Shiraishi functor and non-Kerov deformation of Macdonald polynomials." European Physical Journal C 80, no. 10 (October 2020). http://dx.doi.org/10.1140/epjc/s10052-020-08540-4.

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AbstractWe suggest a further generalization of the hypergeometric-like series due to M. Noumi and J. Shiraishi by substituting the Pochhammer symbol with a nearly arbitrary function. Moreover, this generalization is valid for the entire Shiraishi series, not only for its Noumi–Shiraishi part. The theta function needed in the recently suggested description of the double-elliptic systems [Awata et al. JHEP 2020:150, arXiv:2005.10563, (2020)], 6d N = 2* SYM instanton calculus and the doubly-compactified network models, is a very particular member of this huge family. The series depends on two kinds of variables, $$\vec {x}$$ x → and $$\vec {y}$$ y → , and on a set of parameters, which becomes infinitely large now. Still, one of the parameters, p is distinguished by its role in the series grading. When $$\vec {y}$$ y → are restricted to a discrete subset labeled by Young diagrams, the series multiplied by a monomial factor reduces to a polynomial at any given order in p. All this makes the map from functions to the hypergeometric-like series very promising, and we call it Shiraishi functor despite it remains to be seen, what are exactly the morphisms that it preserves. Generalized Noumi–Shiraishi (GNS) symmetric polynomials inspired by the Shiraishi functor in the leading order in p can be obtained by a triangular transform from the Schur polynomials and possess an interesting grading. They provide a family of deformations of Macdonald polynomials, as rich as the family of Kerov functions, still very different from them, and, in fact, much closer to the Macdonald polynomials. In particular, unlike the Kerov case, these polynomials do not depend on the ordering of Young diagrams in the triangular expansion.
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28

Minahan, Joseph, Usman Naseer, and Charles Thull. "Conformal field theories on deformed spheres, anomalies, and supersymmetry." SciPost Physics 10, no. 3 (March 10, 2021). http://dx.doi.org/10.21468/scipostphys.10.3.063.

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We study the free energy of four-dimensional CFTs on deformed spheres. For generic nonsupersymmetric CFTs only the coefficient of the logarithmic divergence in the free energy is physical, which is an extremum for the round sphere. We then specialize to N=2N=2 SCFTs where one can preserve some supersymmetry on a compact manifold by turning on appropriate background fields. For deformations of the round sphere the cc anomaly receives corrections proportional to the supersymmetric completion of the (Weyl)^22 term, which we determine up to one constant by analyzing the scale dependence of various correlators in the stress-tensor multiplet. We further show that the double derivative of the free energy with respect to the marginal couplings is proportional to the two-point function of the bottom components of the marginal chiral multiplet placed at the two poles of the deformed sphere. We then use anomaly considerations and counter-terms to parametrize the finite part of the free energy which makes manifest its dependence on the Kähler potential. We demonstrate these results for a theory with a vector multiplet and a massless adjoint hypermultiplet using results from localization. Finally, by choosing a special value of the hypermultiplet mass where the free energy is independent of the deformation, we derive an infinite number of constraints between various integrated correlators in N=4N=4 super Yang-Mills with any gauge group and at all values of the coupling, extending previous results.
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