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 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.

scholarly journals $$ \mathcal{N} $$ = 2 Conformal SYM theories at large $$ \mathcal{N} $$

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
M. Beccaria ◽  
M. Billò ◽  
F. Galvagno ◽  
A. Hasan ◽  
A. Lerda
Keyword(s):  
Matrix Model ◽  
Flat Space ◽  
Finite Radius ◽  
Four Dimensions ◽  
Hooft Coupling ◽  
Planar Limit ◽  
Coupling Behavior ◽  
Algebra Approach ◽  
The Matrix ◽  
Holographic Duals

Abstract We consider a class of $$ \mathcal{N} $$ N = 2 conformal SU(N) SYM theories in four dimensions with matter in the fundamental, two-index symmetric and anti-symmetric representations, and study the corresponding matrix model provided by localization on a sphere S4, which also encodes information on flat-space observables involving chiral operators and circular BPS Wilson loops. We review and improve known techniques for studying the matrix model in the large-N limit, deriving explicit expressions in perturbation theory for these observables. We exploit both recursive methods in the so-called full Lie algebra approach and the more standard Cartan sub-algebra approach based on the eigenvalue distribution. The sub-class of conformal theories for which the number of fundamental hypermultiplets does not scale with N differs in the planar limit from the $$ \mathcal{N} $$ N = 4 SYM theory only in observables involving chiral operators of odd dimension. In this case we are able to derive compact expressions which allow to push the small ’t Hooft coupling expansion to very high orders. We argue that the perturbative series have a finite radius of convergence and extrapolate them numerically to intermediate couplings. This is preliminary to an analytic investigation of the strong coupling behavior, which would be very interesting given that for such theories holographic duals have been proposed.

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 Cubic constraints for the resolvents of the ABJM matrix model and its cousins

2017 ◽  
Vol 32 (11) ◽  
pp. 1750056 ◽  
Author(s):  
H. Itoyama ◽  
T. Oota ◽  
Takao Suyama ◽  
R. Yoshioka
Keyword(s):  
Matrix Models ◽  
Matrix Model ◽  
Lens Space ◽  
Planar Limit ◽  
Number Formula ◽  
Space Matrix ◽  
Chern Simons

A set of Schwinger–Dyson equations forming constraints for at most three resolvent functions are considered for a class of Chern–Simons matter matrix models with two nodes labeled by a nonvanishing number [Formula: see text]. The two cases [Formula: see text] and [Formula: see text] label, respectively, the ABJM matrix model, which is the hyperbolic lift of the affine [Formula: see text] quiver matrix model, and the lens space matrix model. In the planar limit, we derive two cubic loop equations for the two planar resolvents. One of these reduces to the quadratic one when [Formula: see text].

FERMIONS IN THE TOPOLOGICAL EXPANSION OF MATRIX MODELS

1991 ◽  
Vol 06 (09) ◽  
pp. 781-787
Author(s):  
G. FERRETTI
Keyword(s):  
Free Energy ◽  
Matrix Models ◽  
Matrix Model ◽  
Hermitian Matrix ◽  
Coupling Constant ◽  
Counting Problem ◽  
Planar Limit ◽  
Quartic Interaction ◽  
Hermitian Matrix Model ◽  
Topological Expansion

The hermitian matrix model with quartic interaction is studied in presence of fermionic variables. We obtain the contribution to the free energy due to the presence of fermions. The first two terms beyond the planar limit are explicitly found for all values of the coupling constant g. These terms represent the solution of the counting problem for vacuum diagrams with one or two fermionic loops.

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.

Toward a relational matrix model of avatar-mediated interactions.

2019 ◽  
Vol 8 (3) ◽  
pp. 287-295 ◽  
Author(s):  
Jaime Banks ◽  
Caleb T. Carr
Keyword(s):  
Matrix Model

Developing the basis of the matrix model of the regional innovation subsystem

2020 ◽  
Vol 18 (11) ◽  
pp. 2183-2204
Author(s):  
E.I. Moskvitina
Keyword(s):  
Russian Federation ◽  
Matrix Model ◽  
Federal District ◽  
Assessment Method ◽  
Expert Assessment ◽  
Regional Innovation ◽  
Regional Strategies ◽  
Analysis And Synthesis ◽  
The Matrix ◽  
The Russian Federation

Subject. This article deals with the issues related to the formation and implementation of the innovation capacity of the Russian Federation subjects. Objectives. The article aims to develop the organizational and methodological foundations for the formation of a model of the regional innovation subsystem. Methods. For the study, I used the methods of analysis and synthesis, economics and statistics analysis, and the expert assessment method. Results. The article presents a developed basis of the regional innovation subsystem matrix model. It helps determine the relationship between the subjects and the parameters of the regional innovation subsystem. To evaluate the indicators characterizing the selected parameters, the Volga Federal District regions are considered as a case study. The article defines the process of reconciliation of interests between the subjects of regional innovation. Conclusions. The results obtained can be used by regional executive bodies when developing regional strategies for the socio-economic advancement of the Russian Federation subjects.

5-Benzylidene-4-Oxazolidinones are Synergistic with Antibiotics for the Treatment of Staphylococcus Aureus Biofilms

2019 ◽  
Author(s):  
Bram Frohock ◽  
Jessica M. Gilbertie ◽  
Jennifer C. Daiker ◽  
Lauren V. Schnabel ◽  
Joshua Pierce
Keyword(s):  
Staphylococcus Aureus ◽  
Human Health ◽  
Matrix Model ◽  
Bacterial Load ◽  
Collagen Matrix ◽  
Resistance Mechanisms ◽  
Novel Therapeutics ◽  
Innovative Treatment ◽  
Antibiotic Action ◽  
Biofilm Infection

<div>The failure of frontline antibiotics in the clinic is one of the most serious threats to human health and requires a multitude of novel therapeutics and innovative treatment approaches to curtail the growing crisis. In addition to traditional resistance mechanisms resulting in the lack of efficacy of many antibiotics, most chronic and recurring infections are further made tolerant to antibiotic action by the presence of biofilms. Herein, we report an expanded set of 5-benzylidene-4-oxazolidinones that are able to inhibit the formation of Staphylococcus aureus biofilms, disperse preformed biofilms and in combination with common antibiotics are able to significantly reduce the bacterial load in a robust collagen-matrix model of biofilm infection.</div>

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