scholarly journals On the planar limit of 3d $$ {\mathrm{T}}_{\rho}^{\sigma}\left[\mathrm{SU}\left(\mathrm{N}\right)\right] $$

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Lorenzo Coccia ◽  
Christoph F. Uhlemann
Keyword(s):  
Saddle Point ◽  
Matrix Model ◽  
Gauge Theories ◽  
Free Energies ◽  
Planar Limit

Abstract We discuss a limit of 3d $$ {T}_{\rho}^{\sigma}\left[\mathrm{SU}(N)\right] $$ T ρ σ SU N quiver gauge theories in which the number of nodes is large and the ranks scale quadratically with the length of the quiver. The sphere free energies and topologically twisted indices are obtained using supersymmetric localization. Both scale quartically with the length of the quiver and quadratically with N, with trilogarithm functions depending on the quiver data as coefficients. The IR SCFTs have well-behaved supergravity duals in Type IIB, and the free energies match precisely with holographic results. Previously discussed theories with N2 ln N scaling arise as limiting cases. Each balanced 3d quiver theory is linked to a 5d parent, whose matrix model is related and dominated by the same saddle point, leading to close relations between BPS observables.

scholarly journals Strong-coupling results for $$ \mathcal{N} $$ = 2 superconformal quivers and holography

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
M. Billò ◽  
M. Frau ◽  
F. Galvagno ◽  
A. Lerda ◽  
A. Pini
Keyword(s):  
Strong Coupling ◽  
Matrix Model ◽  
Numerical Evaluation ◽  
Gauge Theories ◽  
Four Dimensions ◽  
Hooft Coupling ◽  
Planar Limit ◽  
The Matrix ◽  
Single Trace ◽  
Holographic Description

Abstract We consider $$ \mathcal{N} $$ N = 2 superconformal quiver gauge theories in four dimensions and evaluate the chiral/anti-chiral correlators of single-trace operators. We show that it is convenient to form particular twisted and untwisted combinations of these operators suggested by the dual holographic description of the theory. The various twisted sectors are orthogonal and the correlators in each sector have always the same structure, as we show at the lowest orders in perturbation theory with Feynman diagrams. Using localization we then map the computation to a matrix model. In this way we are able to obtain formal expressions for the twisted correlators in the planar limit that are valid for all values of the ‘t Hooft coupling λ, and find that they are proportional to 1/λ at strong coupling. We successfully test the correctness of our extrapolation against a direct numerical evaluation of the matrix model and argue that the 1/λ behavior qualitatively agrees with the holographic description.

scholarly journals Multiple phases in a generalized Gross-Witten-Wadia matrix model

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Jorge G. Russo ◽  
Miguel Tierz
Keyword(s):  
Partition Function ◽  
Matrix Models ◽  
Characteristic Polynomial ◽  
Matrix Model ◽  
Phase Structure ◽  
Unitary Matrix ◽  
Two Dimensional ◽  
Toeplitz Determinants ◽  
Dimensional Parameter ◽  
Planar Limit

Abstract We study a unitary matrix model of the Gross-Witten-Wadia type, extended with the addition of characteristic polynomial insertions. The model interpolates between solvable unitary matrix models and is the unitary counterpart of a deformed Cauchy ensemble. Exact formulas for the partition function and Wilson loops are given in terms of Toeplitz determinants and minors and large N results are obtained by using Szegö theorem with a Fisher-Hartwig singularity. In the large N (planar) limit with two scaled couplings, the theory exhibits a surprisingly intricate phase structure in the two-dimensional parameter space.

MATRIX MODELS AND MARGINAL OPERATORS IN THE PLANAR LIMIT

1990 ◽  
Vol 05 (24) ◽  
pp. 1927-1932 ◽  
Author(s):  
GIOVANNI M. CICUTA ◽  
EMILIO MONTALDI
Keyword(s):  
Saddle Point ◽  
Matrix Models ◽  
Interaction Potential ◽  
Point Method ◽  
Saddle Point Method ◽  
Planar Limit

The role of monomials which are power of traces of matrices in matrix models with polynomial interaction potential is examined. Because of well-known factorization properties, the density of eigenvalues is trivially obtained in the planar limit by the saddle point method. Different susceptibilities have positive or negative critical coefficients.

scholarly journals N=2supersymmetricSO(N)/Sp(N)gauge theories from the matrix model

2003 ◽  
Vol 67 (10) ◽  
Author(s):  
Changhyun Ahn ◽  
Soonkeon Nam
Keyword(s):  
Matrix Model ◽  
Gauge Theories ◽  
The Matrix

Deffect free energies in lattice gauge theories with matter fields

1984 ◽  
Vol 230 (4) ◽  
pp. 407-434 ◽  
Author(s):  
Jean Bricmont ◽  
Jürg Fröhlich
Keyword(s):  
Gauge Theories ◽  
Free Energies ◽  
Lattice Gauge ◽  
Lattice Gauge Theories ◽  
Matter Fields

scholarly journals Analyticity of the Planar Limit of a Matrix Model

2012 ◽  
Vol 14 (3) ◽  
pp. 499-565 ◽  
Author(s):  
Stavros Garoufalidis ◽  
Ionel Popescu
Keyword(s):  
Matrix Model ◽  
Planar Limit

scholarly journals EFFECTIVE SUPERPOTENTIALS FOR SO/Sp WITH FLAVOR FROM MATRIX MODELS

2003 ◽  
Vol 18 (16) ◽  
pp. 1113-1126 ◽  
Author(s):  
YUTAKA OOKOUCHI ◽  
YOSHIYUKI WATABIKI
Keyword(s):  
Matrix Models ◽  
Matrix Model ◽  
Gauge Theories ◽  
Tree Level ◽  
Arbitrary Tree

We study matrix models related to SO/Sp gauge theories with flavors. We give the effective superpotentials for gauge theories with arbitrary tree level superpotential up to first instanton level. For quartic tree level superpotential, we obtained exact one-cut solution. We also derive Seiberg–Witten curve for these gauge theories from matrix model argument.

LONG DISTANCE DYNAMICS AND CONFINEMENT VIA RG DECIMATIONS

2009 ◽  
Vol 24 (34) ◽  
pp. 2717-2730 ◽  
Author(s):  
E. T. TOMBOULIS
Keyword(s):  
Fixed Point ◽  
Renormalization Group ◽  
Gauge Theory ◽  
Gauge Theories ◽  
Upper And Lower Bounds ◽  
Free Energies ◽  
Long Distance ◽  
Strongly Coupled ◽  
Four Dimensions ◽  
Lattice Regularization

We review a recently developed framework employing computable Renormalization Group (RG) decimations for gauge theories in the lattice regularization. They provide upper and lower bounds at every scale for free energies and some order parameters. By interpolating between these bounds representations of the exact quantities are obtained at progressively longer scales (coarser lattices). In the case of the SU(2) gauge theory in four dimensions RG flow to the confining strongly coupled regime is obtained for any initial coupling; whereas for the U(1) theory a fixed point is reached for small initial coupling.

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