scholarly journals Supersymmetric phases of 4d $$ \mathcal{N} $$ = 4 SYM at large N

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Alejandro Cabo-Bizet ◽  
Sameer Murthy
Keyword(s):  
Black Hole ◽  
Matrix Model ◽  
Modular Forms ◽  
Chemical Potential ◽  
Saddle Points ◽  
Yang Mills ◽  
Point Configurations ◽  
Large N ◽  
The Matrix ◽  
Real Analytic

Abstract We find a family of complex saddle-points at large N of the matrix model for the superconformal index of SU(N ) $$ \mathcal{N} $$ N = 4 super Yang-Mills theory on S3× S1 with one chemical potential τ . The saddle-point configurations are labelled by points (m, n) on the lattice Λτ = ℤτ + ℤ with gcd(m, n) = 1. The eigenvalues at a given saddle are uniformly distributed along a string winding (m, n) times along the (A, B) cycles of the torus ℂ/Λτ . The action of the matrix model extended to the torus is closely related to the Bloch-Wigner elliptic dilogarithm, and the related Bloch formula allows us to calculate the action at the saddle-points in terms of real-analytic Eisenstein series. The actions of (0, 1) and (1, 0) agree with that of pure AdS5 and the supersymmetric AdS5 black hole, respectively. The black hole saddle dominates the canonical ensemble when τ is close to the origin, and there are new saddles that dominate when τ approaches rational points. The extension of the action in terms of modular forms leads to a simple treatment of the Cardy-like limit τ → 0.

scholarly journals THE HAGEDORN TRANSITION AND THE MATRIX MODEL FOR STRINGS

1998 ◽  
Vol 13 (26) ◽  
pp. 2085-2094 ◽  
Author(s):  
B. SATHIAPALAN
Keyword(s):  
Matrix Model ◽  
Light Cone ◽  
Degrees Of Freedom ◽  
Low Energy ◽  
Matrix Formalism ◽  
Yang Mills ◽  
Large N ◽  
The Matrix ◽  
The Continuum ◽  
String Worldsheet

We use the matrix formalism to investigate what happens to strings above the Hagedorn temperature. We show that is not a limiting temperature but a temperature at which the continuum string picture breaks down. We study a collection of N D-0-branes arranged to form a string having N units of light-cone momentum. We find that at high temperatures the favored phase is one where the string worldsheet has disappeared and the low-energy degrees of freedom consists of N2 massless particles ("gluons"). The nature of the transition is very similar to the deconfinement transition in large-N Yang–Mills theories.

scholarly journals THE AREA LAW IN MATRIX MODELS FOR LARGE N QCD STRINGS

2002 ◽  
Vol 13 (04) ◽  
pp. 555-563 ◽  
Author(s):  
K. N. ANAGNOSTOPOULOS ◽  
W. BIETENHOLZ ◽  
J. NISHIMURA
Keyword(s):  
Numerical Simulations ◽  
Matrix Models ◽  
Matrix Model ◽  
Hermitian Matrices ◽  
Yang Mills ◽  
Loop Area ◽  
Large N ◽  
Volume Limit ◽  
The Matrix ◽  
Area Law

We study the question whether matrix models obtained in the zero volume limit of 4d Yang–Mills theories can describe large N QCD strings. The matrix model we use is a variant of the Eguchi–Kawai model in terms of Hermitian matrices, but without any twists or quenching. This model was originally proposed as a toy model of the IIB matrix model. In contrast to common expectations, we do observe the area law for Wilson loops in a significant range of scale of the loop area. Numerical simulations show that this range is stable as N increases up to 768, which strongly suggests that it persists in the large N limit. Hence the equivalence to QCD strings may hold for length scales inside a finite regime.

scholarly journals D-Brane Configurations and Nicolai Map in Supersymmetric Yang–Mills Theory

1997 ◽  
Vol 12 (03) ◽  
pp. 183-193 ◽  
Author(s):  
I. I. Kogan ◽  
R. J. Szabo ◽  
G. W. Semenoff
Keyword(s):  
Quantum Mechanics ◽  
Phase Transitions ◽  
Matrix Model ◽  
Short Distance ◽  
Dimensional Theory ◽  
Yang Mills ◽  
Large N ◽  
The Matrix ◽  
M Theory ◽  
Matrix Quantum

We discuss some properties of a supersymmetric matrix model that is the dimensional reduction of supersymmetric Yang–Mills theory in 10 dimensions and which has been recently argued to represent the short-distance structure of M-theory in the infinite momentum frame. We describe a reduced version of the matrix quantum mechanics and derive the Nicolai map of the simplified supersymmetric matrix model. We use this to argue that there are no phase transitions in the large-N limit, and hence that S-duality is preserved in the full 11-dimensional theory.

scholarly journals Exact 1/N expansion of Wilson loop correlators in $$ \mathcal{N} $$ = 4 Super-Yang-Mills theory

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Wolfgang Mück
Keyword(s):  
Matrix Model ◽  
Wilson Loop ◽  
Model Solution ◽  
Wilson Loops ◽  
Combinatorial Formula ◽  
Expectation Value ◽  
Yang Mills ◽  
Hooft Coupling ◽  
The Matrix ◽  
Super Yang Mills Theory

Abstract Supersymmetric circular Wilson loops in $$ \mathcal{N} $$ N = 4 Super-Yang-Mills theory are discussed starting from their Gaussian matrix model representations. Previous results on the generating functions of Wilson loops are reviewed and extended to the more general case of two different loop contours, which is needed to discuss coincident loops with opposite orientations. A combinatorial formula representing the connected correlators of multiply wound Wilson loops in terms of the matrix model solution is derived. Two new results are obtained on the expectation value of the circular Wilson loop, the expansion of which into a series in 1/N and to all orders in the ’t Hooft coupling λ was derived by Drukker and Gross about twenty years ago. The connected correlators of two multiply wound Wilson loops with arbitrary winding numbers are calculated as a series in 1/N. The coefficient functions are derived not only as power series in λ, but also to all orders in λ by expressing them in terms of the coefficients of the Drukker and Gross series. This provides an efficient way to calculate the 1/N series, which can probably be generalized to higher-point correlators.

PHASE DIAGRAM AND ORTHOGONAL POLYNOMIALS IN MULTIPLE-WELL MATRIX MODELS

1991 ◽  
Vol 06 (25) ◽  
pp. 4491-4515 ◽  
Author(s):  
OLAF LECHTENFELD ◽  
RASHMI RAY ◽  
ARUP RAY
Keyword(s):  
Phase Diagram ◽  
Orthogonal Polynomials ◽  
Matrix Models ◽  
Matrix Model ◽  
Phase Structure ◽  
Saddle Points ◽  
Tree Level ◽  
Potential Wells ◽  
Large N

We investigate a zero-dimensional Hermitian one-matrix model in a triple-well potential. Its tree-level phase structure is analyzed semiclassically as well as in the framework of orthogonal polynomials. Some multiple-arc eigenvalue distributions in the first method correspond to quasiperiodic large-N behavior of recursion coefficients for the second. We further establish this connection between the two approaches by finding three-arc saddle points from orthogonal polynomials. The latter require a modification for nondegenerate potential minima; we propose weighing the average over potential wells.

scholarly journals Effective Action and Measure in Matrix Model of IIB Superstrings

1997 ◽  
Vol 12 (31) ◽  
pp. 2331-2340 ◽  
Author(s):  
L. Chekhov ◽  
K. Zarembo
Keyword(s):  
Matrix Model ◽  
Effective Action ◽  
Continuum Limit ◽  
Auxiliary Field ◽  
Large N ◽  
The Matrix ◽  
Reparametrization Invariance ◽  
The Continuum ◽  
Induced Measure

We calculate an effective action and measure induced by the integration over the auxiliary field in the matrix model recently proposed to describe IIB superstrings. It is shown that the measure of integration over the auxiliary matrix is uniquely determined by locality and reparametrization invariance of the resulting effective action. The large-N limit of the induced measure for string coordinates is discussed in detail. It is found to be ultralocal and, thus, is possibly irrelevant in the continuum limit. The model of the GKM type is considered in relation to the effective action problem.

TOPOLOGICAL σ MODELS AND LARGE N MATRIX INTEGRAL

1995 ◽  
Vol 10 (29) ◽  
pp. 4203-4224 ◽  
Author(s):  
TOHRU EGUCHI ◽  
KENTARO HORI ◽  
SUNG-KIL YANG
Keyword(s):  
Matrix Model ◽  
Riemann Surfaces ◽  
Holomorphic Maps ◽  
Integrable Structure ◽  
Toda Hierarchy ◽  
Matrix Integral ◽  
Large N ◽  
The Matrix ◽  
Lax Operator ◽  
The One

In this paper we describe in some detail the representation of the topological CP1 model in terms of a matrix integral which we have introduced in a previous article. We first discuss the integrable structure of the CP1 model and show that it is governed by an extension of the one-dimensional Toda hierarchy. We then introduce a matrix model which reproduces the sum over holomorphic maps from arbitrary Riemann surfaces onto CP1. We compute intersection numbers on the moduli space of curves using a geometrical method and show that the results agree with those predicted by the matrix model. We also develop a Landau-Ginzburg (LG) description of the CP1 model using a superpotential eX + et0,Q e-X given by the Lax operator of the Toda hierarchy (X is the LG field and t0,Q is the coupling constant of the Kähler class). The form of the superpotential indicates the close connection between CP1 and N=2 supersymmetric sine-Gordon theory which was noted sometime ago by several authors. We also discuss possible generalizations of our construction to other manifolds and present an LG formulation of the topological CP2 model.

scholarly journals Testing the holographic principle using lattice simulations

2018 ◽  
Vol 175 ◽  
pp. 08004 ◽  
Author(s):  
Raghav G. Jha ◽  
Simon Catterall ◽  
David Schaich ◽  
Toby Wiseman
Keyword(s):  
Phase Transition ◽  
Black Hole ◽  
Strong Coupling ◽  
Type Ii ◽  
Two Dimensional ◽  
Yang Mills ◽  
Large N ◽  
Gauge Gravity ◽  
Gravity Duality ◽  
Made In

The lattice studies of maximally supersymmetric Yang-Mills (MSYM) theory at strong coupling and large N is important for verifying gauge/gravity duality. Due to the progress made in the last decade, based on ideas from topological twisting and orbifolding, it is now possible to study these theories on the lattice while preserving an exact supersymmetry on the lattice. We present some results from the lattice studies of two-dimensional MSYM which is related to Type II supergravity. Our results agree with the thermodynamics of different black hole phases on the gravity side and the phase transition (Gregory–Laflamme) between them.

scholarly journals CRITICAL SCALING IN THE MATRIX MODEL ON A BETHE TREE

1994 ◽  
Vol 09 (21) ◽  
pp. 1963-1973 ◽  
Author(s):  
D.V. BOULATOV
Keyword(s):  
Matrix Model ◽  
Explicit Solutions ◽  
Critical Scaling ◽  
Edge Singularity ◽  
Large N ◽  
The Matrix

The matrix model with a Bethe tree embedding space (coincides at large N with the Kazakov-Migdal “induced QCD” model1) is investigated. We further elaborate the Riemann-Hilbert approach of Ref. 2 assuming certain holomorphic properties of the solution. The critical scaling (an edge singularity of the density) is found to be [Formula: see text][Formula: see text] arccos D, for |D|<1, and [Formula: see text] arccos [Formula: see text] for D>1. Explicit solutions are constructed at D=1/2 and D=∞.

scholarly journals Fundamental Strings and D-Strings in the IIB Matrix Model

1997 ◽  
Vol 12 (18) ◽  
pp. 1301-1315 ◽  
Author(s):  
B. Sathiapalan
Keyword(s):  
Matrix Model ◽  
Scaling Limit ◽  
Duality Group ◽  
Fundamental String ◽  
Large N ◽  
The Matrix ◽  
Model Derivation ◽  
The One ◽  
The Right ◽  
String Worldsheet

The matrix model for IIB superstring proposed by Ishibashi, Kawai, Kitazawa and Tsuchiya is investigated. Consideration of planar and non-planar diagrams suggests that large-N perturbative expansion is consistent with the double scaling limit proposed by the above authors. We write down a Wilson loop that can be interpreted as a fundamental string vertex operator. The one-point tadpole in the presence of a D-string has the right form and this can be viewed as a matrix model derivation of the boundary conditions that define a D-string. We also argue that if worldsheet coordinates σ and τ are introduced to the fundamental string, then the conjugate variable d/dσ and d/dτ can be interpreted as the D-string worldsheet coordinates. In this way the SL (2Z) duality group of the IIB superstring becomes identified with the symplectic group acting on (p,q).

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