scholarly journals N=4super Yang-Mills theory from the plane wave matrix model

2008 ◽  
Vol 78 (10) ◽  
Author(s):  
Takaaki Ishii ◽  
Goro Ishiki ◽  
Shinji Shimasaki ◽  
Asato Tsuchiya
Keyword(s):  
Plane Wave ◽  
Matrix Model ◽  
Yang Mills

scholarly journals BOUNCES/DYONS IN THE PLANE WAVE MATRIX MODEL AND SU(N) YANG–MILLS THEORY

2009 ◽  
Vol 24 (05) ◽  
pp. 349-359 ◽  
Author(s):  
ALEXANDER D. POPOV
Keyword(s):  
Plane Wave ◽  
Matrix Model ◽  
Gauge Fields ◽  
Field Tensor ◽  
Flux Tubes ◽  
Yang Mills ◽  
Electric And Magnetic Fields ◽  
Inverse Radius ◽  
Minkowski Signature ◽  
Double Well Potential

We consider SU (N) Yang–Mills theory on the space ℝ × S3 with Minkowski signature (-+++). The condition of SO(4)-invariance imposed on gauge fields yields a bosonic matrix model which is a consistent truncation of the plane wave matrix model. For matrices parametrized by a scalar ϕ, the Yang–Mills equations are reduced to the equation of a particle moving in the double-well potential. The classical solution is a bounce, i.e. a particle which begins at the saddle point ϕ = 0 of the potential, bounces off the potential wall and returns to ϕ = 0. The gauge field tensor components parametrized by ϕ are smooth and for finite time, both electric and magnetic fields are nonvanishing. The energy density of this non-Abelian dyon configuration does not depend on coordinates of ℝ × S3 and the total energy is proportional to the inverse radius of S3. We also describe similar bounce dyon solutions in SU (N) Yang–Mills theory on the space ℝ × S2 with signature (-++). Their energy is proportional to the square of the inverse radius of S2. From the viewpoint of Yang–Mills theory on ℝ1,1 × S2 these solutions describe non-Abelian (dyonic) flux tubes extended along the x3-axis.

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.

scholarly journals On topological recursion for Wilson loops in $$ \mathcal{N} $$ = 4 SYM at strong coupling

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
M. Beccaria ◽  
A. Hasan
Keyword(s):  
Strong Coupling ◽  
Matrix Model ◽  
Wilson Loops ◽  
Expectation Value ◽  
Yang Mills ◽  
Usual Procedure ◽  
Topological Recursion ◽  
Sample Application ◽  
Single Trace ◽  
Genus Expansion

Abstract We consider U(N) $$ \mathcal{N} $$ N = 4 super Yang-Mills theory and discuss how to extract the strong coupling limit of non-planar corrections to observables involving the $$ \frac{1}{2} $$ 1 2 -BPS Wilson loop. Our approach is based on a suitable saddle point treatment of the Eynard-Orantin topological recursion in the Gaussian matrix model. Working directly at strong coupling we avoid the usual procedure of first computing observables at finite planar coupling λ, order by order in 1/N, and then taking the λ ≫ 1 limit. In the proposed approach, matrix model multi-point resolvents take a simplified form and some structures of the genus expansion, hardly visible at low order, may be identified and rigorously proved. As a sample application, we consider the expectation value of multiple coincident circular supersymmetric Wilson loops as well as their correlator with single trace chiral operators. For these quantities we provide novel results about the structure of their genus expansion at large tension, generalising recent results in arXiv:2011.02885.

scholarly journals Thermal phase transition in Yang-Mills matrix model

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Georg Bergner ◽  
Norbert Bodendorfer ◽  
Masanori Hanada ◽  
Enrico Rinaldi ◽  
Andreas Schäfer ◽  
...  
Keyword(s):  
Phase Transition ◽  
Matrix Model ◽  
Yang Mills ◽  
Thermal Phase Transition ◽  
Thermal Phase

scholarly journals Non-commutative Yang–Mills in IIB matrix model

2000 ◽  
Vol 565 (1-2) ◽  
pp. 176-192 ◽  
Author(s):  
Hajime Aoki ◽  
Nobuyuki Ishibashi ◽  
Satoshi Iso ◽  
Hikaru Kawai ◽  
Yoshihisa Kitazawa ◽  
...  
Keyword(s):  
Matrix Model ◽  
Yang Mills

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 Quantum phases of Yang-Mills matrix model coupled to fundamental fermions

2017 ◽  
Vol 58 (2) ◽  
pp. 022103 ◽  
Author(s):  
Mahul Pandey ◽  
Sachindeo Vaidya
Keyword(s):  
Matrix Model ◽  
Quantum Phases ◽  
Yang Mills
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