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Добірка наукової літератури з теми "Yang-Mills matrix model"

Автор: Grafiati

Опубліковано: 6 вересня 2023

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Статті в журналах з теми "Yang-Mills matrix model"

Aoki, Hajime, Nobuyuki Ishibashi, Satoshi Iso, Hikaru Kawai, Yoshihisa Kitazawa, and Tsukasa Tada. "Non-commutative Yang–Mills in IIB matrix model." Nuclear Physics B 565, no. 1-2 (January 2000): 176–92. http://dx.doi.org/10.1016/s0550-3213(99)00633-1.

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Pandey, Mahul, and Sachindeo Vaidya. "Yang–Mills matrix mechanics and quantum phases." International Journal of Geometric Methods in Modern Physics 14, no. 08 (May 11, 2017): 1740009. http://dx.doi.org/10.1142/s0219887817400096.

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Анотація:

The [Formula: see text] Yang–Mills matrix model coupled to fundamental fermions is studied in the adiabatic limit, and quantum critical behavior is seen at special corners of the gauge field configuration space. The quantum scalar potential for the gauge field induced by the fermions diverges at the corners, and is intimately related to points of enhanced degeneracy of the fermionic Hamiltonian. This in turn leads to superselection sectors in the Hilbert space of the gauge field, the ground states in different sectors being orthogonal to each other. The [Formula: see text] Yang–Mills matrix model coupled to two Weyl fermions has three quantum phases. When coupled to a massless Dirac fermion, the number of quantum phases is four. One of these phases is the color-spin locked phase. This paper is an extended version of the lectures given by the second author (SV) at the International Workshop on Quantum Physics: Foundations and Applications, Bangalore, in February 2016, and is based on [1].

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Siegel, W. "Super Yang-Mills theory as a random matrix model." Physical Review D 52, no. 2 (July 15, 1995): 1035–41. http://dx.doi.org/10.1103/physrevd.52.1035.

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Kimura, Yusuke, and Yoshihisa Kitazawa. "Supercurrent interactions in noncommutative Yang–Mills and IIB matrix model." Nuclear Physics B 598, no. 1-2 (March 2001): 73–86. http://dx.doi.org/10.1016/s0550-3213(00)00785-9.

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Xu, Feng. "A Random Matrix Model From Two Dimensional Yang-Mills Theory." Communications in Mathematical Physics 190, no. 2 (December 1, 1997): 287–307. http://dx.doi.org/10.1007/s002200050242.

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Acharyya, Nirmalendu, A. P. Balachandran, Mahul Pandey, Sambuddha Sanyal, and Sachindeo Vaidya. "Glueball spectra from a matrix model of pure Yang–Mills theory." International Journal of Modern Physics A 33, no. 13 (May 9, 2018): 1850073. http://dx.doi.org/10.1142/s0217751x18500732.

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Анотація:

We present variational estimates for the low-lying energies of a simple matrix model that approximates SU(3) Yang–Mills theory on a three-sphere of radius R. By fixing the ground state energy, we obtain the (integrated) renormalization group (RG) equation for the Yang–Mills coupling g as a function of R. This RG equation allows to estimate the mass of other glueball states, which we find to be in excellent agreement with lattice simulations.

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CHAN, HONG-MO. "YANG–MILLS DUALITY AS THE ORIGIN OF FERMION GENERATIONS." Modern Physics Letters A 18, no. 08 (March 14, 2003): 537–43. http://dx.doi.org/10.1142/s0217732303009629.

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A non-Abelian extension of electric-magnetic duality implies that dual to confined colour SU(3), there also ought to be a broken threefold symmetry which can play the role of fermion generations. A model constructed on these premises not only gives a raison d'être for 3 and only 3 generations as observed but also offers a natural explanation for the distinctive fermion mass and mixing patterns seen in experiment. A calculation to one-loop order in this model with only 3 fitted parameters already gives correct values, all within present experimental errors, for the following quantities: the mass ratios mc/mt, ms/mb, mμ/mτ, all 9 matrix elements of the CKM mixing matrix |Vrs| for quarks, plus the lepton MNS mixing matrix elements |Uμ3| and |Ue3| studied in neutrino oscillation experiments with respectively atmospheric and reactor neutrinos.

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Pandey, Mahul, and Sachindeo Vaidya. "Quantum phases of Yang-Mills matrix model coupled to fundamental fermions." Journal of Mathematical Physics 58, no. 2 (February 2017): 022103. http://dx.doi.org/10.1063/1.4976503.

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Kawamoto, Shoichi, and Dan Tomino. "A renormalization group approach to a Yang–Mills two matrix model." Nuclear Physics B 877, no. 3 (December 2013): 825–51. http://dx.doi.org/10.1016/j.nuclphysb.2013.10.021.

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PANZERI, STEFANO. "THE c=1 MATRIX MODEL FORMULATION OF TWO-DIMENSIONAL YANG-MILLS THEORIES." Modern Physics Letters A 08, no. 33 (October 30, 1993): 3201–14. http://dx.doi.org/10.1142/s0217732393002130.

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Анотація:

We find the exact matrix model description of two-dimensional Yang-Mills theories on a cylinder or on a torus and with an arbitrary semisimple compact gauge group. This matrix model is the singlet sector of a c=1 matrix model where the matrix field is in the fundamental representation of the gauge group. We also prove that the basic constituents of the theory are Sutherland fermions in the zero coupling limit, and this leads to an interesting connection between two-dimensional gauge theories and one-dimensional integrable systems. In particular we derive for all the classical groups the exact grand canonical partition function of the free fermion system corresponding to a two-dimensional gauge theory on a torus.

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Більше джерел

Дисертації з теми "Yang-Mills matrix model"

Nesti, Fabrizio. "Aspects of Large N Analysis for the Yang-Mills-Higgs Model and Matrix Models." Doctoral thesis, SISSA, 1996. http://hdl.handle.net/20.500.11767/4513.

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The first part of this work deals with some new large N ideas for the YMH model in three dimensions. Needless to say there is a large historical and scientific background and it is of course difficult to say something really new on these subjects. Nevertheless some latest ideas on matrix models, subject on which I have worked in the first part of my period here at SISSA, are a valuable tool and should find applications in otherwise 'slow' fields. The study of large N model of monopole gas are not investigated, to our knowledge, for example. This work wants to be a starting point for this investigation. Along this analysis we have found many and different problems to think about, the principal is the reason how the Eguchi Kawai works, an issue that also has not been completely clarified, despite of the volume of numerical calculations. After one finds a reliable method for the functional determinant, it will be possible to draw definite conclusions on the large N monopole gas, which seems promising some interesting feature, due to the competition of factors which takes place in the large N limit.

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Hanada, Masanori. "Emergence of spacetime from 2B matrix model and large-N reduced Yang-Mills theories." 京都大学 (Kyoto University), 2007. http://hdl.handle.net/2433/136764.

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Borla, Umberto. "Mass limits for 5-dimensional super Yang-Mills." Thesis, Uppsala universitet, Teoretisk fysik, 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-235752.

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In this thesis we consider the N=1 super Yang-Mills theory on S5 with a single hypermultiplet in the adjoint representation. We argue that there is a critical value of the hypermultiplet mass M=3/2r, where r is the radius of S5, for which the free energy vanishes, and we study the model in the proximity of this value. For large N we provide analytical results for the free energy and the eigenvalue density in the weak and strong coupling limits, and in one case we solve the saddle point equation using a technique introduced by Hoppe. We present numerical results to show where each approximation is justified, and to explore the regimes where the model cannot be solved analytically. Based on the numerical results, we argue that in most cases the behaviour of the model is better understood in terms of an effective coupling constant λ'=λM. For small M the model simplifies to one whose kernel is non-singular. This simplified model shows a peculiar peak structure in the eigenvalue distribution, with the number of peaks growing as the effective coupling is increased. We interpret this as a series of phase transitions as M approaches 3/2r.

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Kanning, Nils. "On the integrable structure of super Yang-Mills scattering amplitudes." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät, 2016. http://dx.doi.org/10.18452/17663.

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Die maximal supersymmetrische Yang-Mills-Theorie im vierdimensionalen Minkowski-Raum ist ein außergewöhnliches Modell der mathematischen Physik. Dies gilt vor allem im planaren Limes, in dem die Theorie integrabel zu sein scheint. So sind etwa ihre Streuamplituden auf Baumgraphenniveau Invarianten einer Yangschen Algebra, die die superkonforme Algebra psu(2,2|4) beinhaltet. Diese unendlichdimmensionale Symmetrie ist ein Kennzeichen für Integrabilität. In dieser Dissertation untersuchen wir Verbindungen zwischen solchen Amplituden und integrablen Modellen, um Grundlagen für eine effiziente, auf der Integrabilität basierende Berechnung von Amplituden zu legen. Dazu charakterisieren wir Yangsche Invarianten innerhalb der Quanten-Inverse-Streumethode, die Werkzeuge zur Behandlung integrabler Spinketten bereitstellt. In diesem Rahmen entwickeln wir Methoden zur Konstruktion Yangscher Invarianten. Wir zeigen, dass der algebraische Bethe-Ansatz für die Erzeugung von Yangschen Invarianten für u(2) anwendbar ist. Die zugehörigen Bethe-Gleichungen lassen sich leicht lösen. Unser Zugang erlaubt es zudem diese Invarianten als Zustandssummen von Vertexmodellen zu interpretieren. Außerdem führen wir ein unitäres Graßmannsches Matrixmodell zur Berechnung Yangscher Invarianten mit Oszillatordarstellungen von u(p,q|m) ein. In einem Spezialfall reduziert es sich zu dem Brezin-Gross-Witten-Model. Wir wenden eine auf Bargmann zurückgehende Integraltransformation auf unser Matrixmodell an, welche die Oszillatoren in Spinor-Helizitäts-artige Variablen überführt. Dadurch gelangen wir zu einer Weiterentwicklung der Graßmann-Integralformulierung bestimmter Amplituden. Die maßgeblichen Unterschiede sind, dass wir in der Minkowski-Signatur arbeiten und die Integrationskontur auf die unitäre Gruppenmannigfaltigkeit festgelegt ist. Wir vergleichen durch unser Integral gegebene Yangsche Invarianten mit Amplituden und kürzlich eingeführten Deformationen derselben.
The maximally supersymmetric Yang-Mills theory in four-dimensional Minkowski space is an exceptional model of mathematical physics. Even more so in the planar limit, where the theory is believed to be integrable. In particular, the tree-level scattering amplitudes were shown to be invariant under the Yangian of the superconformal algebra psu(2,2|4). This infinite-dimensional symmetry is a hallmark of integrability. In this dissertation we explore connections between these amplitudes and integrable models. Our aim is to lay foundations for an efficient integrability-based computation of amplitudes. To this end, we characterize Yangian invariants within the quantum inverse scattering method, which is an extensive toolbox for integrable spin chains. Making use of this setup, we develop methods for the construction of Yangian invariants. We show that the algebraic Bethe ansatz can be specialized to yield Yangian invariants for u(2). Our approach also allows to interpret these Yangian invariants as partition functions of vertex models. What is more, we establish a unitary Graßmannian matrix model for the construction of u(p,q|m) Yangian invariants with oscillator representations. In a special case our formula reduces to the Brezin-Gross-Witten model. We apply an integral transformation due to Bargmann to our unitary Graßmannian matrix model, which turns the oscillators into spinor helicity-like variables. Thereby we are led to a refined version of the Graßmannian integral formula for certain amplitudes. The most decisive differences are that we work in Minkowski signature and that the integration contour is fixed to be a unitary group manifold. We compare Yangian invariants defined by our integral to amplitudes and recently introduced deformations thereof.

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Pandey, Mahul. "A Study of the Low-Energy Spectrum and Phase Structure of a Yang-Mills Matrix Model." Thesis, 2019. https://etd.iisc.ac.in/handle/2005/5120.

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Yang-Mills theory is a non-Abelian gauge theory based on the gauge group SU(N), and lies at the heart of the QCD, the theory underlying strong interactions. Due to the fundamental property of asymptotic freedom, a study of its low-energy spectrum and quantum phase structure requires the application of non-perturbative techniques. Since analytic non-perturbative QCD calculations are notoriously difficult and numerical approaches typically require huge computational resources, a simple model that can capture important non-perturbative information is quite useful. In this thesis, we study a matrix model that is obtained by the reduction of Yang-Mills theory on a 3-sphere of radius R and describes the quantum dynamics of the zero modes of the full quantum field theory. Even though at first glance this is a drastic approximation, we demonstrate that this model successfully captures important nonperturbative aspects of the full quantum field theory, and being a quantum mechanical model, it can be studied using relatively simple analytical and numerical techniques. In the first part of the thesis, we focus our attention to the pure SU(3) gauge theory and make a numerical estimate of the lightest glueball masses in the matrix model. The spectrum of the matrix model Hamiltonian is analyzed in the strong coupling limit using variational calculation, and by employing a suitable renormalization scheme to determine the running of the coupling constant with R, the asymptotic values of the energy eigenvalues in the at space limit is related to the masses of glueballs. Our estimate shows excellent agreement with lattice results, with our values lying within the lattice error bars. We then analyze the matrix model for the gauge field coupled to fermions and make an estimate of the light hadron spectrum using a similar scheme. We find that the matrix model estimates the light hadron spectrum fairly accurately, with most masses falling within 20% of their experimental values. In the second part of the thesis, we analyze the Yang-Mills matrix model in the weak coupling limit. In this regime, the kinetic term for the gauge fields is small compared to that of fermions, so Born-Oppenheimer approximation can be used to quantize the fermions in the background of a constant gauge field, which in turn induce a quantum scalar potential in the effective Hamiltonian governing the dynamics of the gauge fields. This scalar potential has singularities at certain regions of the gauge configuration space and leads to the emergence of superselection sectors in the Hilbert space of gauge fields, which have a natural interpretation as different quantum phases. We examine the phase structure of 2-colour QCD and demonstrate that these phases corresponding to colour-spin locking. We also examine the phase structure of the N = 1 SYM matrix model, and investigate the role that supersymmetry plays in this description.

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Mulokwe, Mbavhalelo. "The large-N limit of matrix models and AdS/CFT." Thesis, 2014.

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Анотація:

Random matrix models have found numerous applications in both Theoretical Physics and Mathematics. In the gauge-gravity duality, for example, the dynamics of the half- BPS sector can be fully described by the holomorphic sector of a single complex matrix model. In this thesis, we study the large-N limit of multi-matrix models at strong-coupling. In particular, we explore the significance of rescaling the matrix fields. In order to investigate this, we consider the matrix quantum mechanics of a single Hermitian system with a quartic interaction. We “compactify” this system on a circle and compute the first-order perturbation theory correction to the ground-state energy. The exact ground-state energy is obtained using the Das-Jevicki-Sakita Collective Field Theory approach. We then discuss the multi-matrix model that results from the compactification of the Higgs sector of N = 4 SYM on S4 (or T S3). For the radial subsector, the saddle-point equations are solved exactly and hence the radial density of eigenvalues for an arbitrary number of even Hermitian matrices is obtained. The single complex matrix model is parametrized in terms of the matrix valued polar coordinates and the first-order perturbation theory density of eigenstates is obtained. We make use of the Harish-Chandra- Itzykson-Zuber (HCIZ) formula to write down the exact saddle-point equations. We then give a complementary approach - based on the Dyson-Schwinger (loop) equations formalism - to the saddle-point method. We reproduce the results obtained for the radial (single matrix) subsector. The two-matrix integral does not close on the original set of variables and thus we map the system onto an auxiliary Penner-type two matrix model. In the absence of a logarithmic potential we derive a radial hemispherical density of eigenvalues. The system is regulated with a logarithm potential, and the Dobroliubov-Makeenko-Semenoff (DMS) loop equations yield an equation of third degree that is satisfied by the generating function. This equation is solved at strong coupling and, accordingly, we obtain the radial density of eigenvalues.

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Частини книг з теми "Yang-Mills matrix model"

"Metropolis Algorithm for Yang–Mills Matrix Models." In Computational Physics, 107–17. WORLD SCIENTIFIC, 2017. http://dx.doi.org/10.1142/9789813200227_0010.

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"Hybrid Monte Carlo Algorithm for Yang—Mills Matrix Models." In Computational Physics, 119–29. WORLD SCIENTIFIC, 2017. http://dx.doi.org/10.1142/9789813200227_0011.

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Тези доповідей конференцій з теми "Yang-Mills matrix model"

Shimasaki, Shinji, Pyungwon Ko, and Deog Ki Hong. "A nonperturbative definition of N = 4 Super Yang-Mills by the plane wave matrix model." In SUPERSYMMETRY AND THE UNIFICATION OF FUNDAMENTAL INTERACTIONS. AIP, 2008. http://dx.doi.org/10.1063/1.3052000.

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Butti, Pietro, Margarita Garcia Perez, Antonio Gonzalez-Arroyo, K.-I. Ishikawa, and M. Okawa. "Scale setting for N = 1 SUSY Yang-Mills at large-N through volume-reduced twisted matrix model." In The 38th International Symposium on Lattice Field Theory. Trieste, Italy: Sissa Medialab, 2022. http://dx.doi.org/10.22323/1.396.0474.

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Blaschke, Daniel. "Special geometries emerging from Yang-Mills type matrix models." In Corfu Summer Institute on Elementary Particles and Physics - Workshop on Non Commutative Field Theory and Gravity. Trieste, Italy: Sissa Medialab, 2011. http://dx.doi.org/10.22323/1.127.0011.

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