scholarly journals THE STUDY OF THE CONTINUUM LIMIT OF THE SUPERSYMMETRIC WARD-TAKAHASHI IDENTITY FOR N = 1 SUPER YANG-MILLS THEORY

2004 ◽  
Author(s):  
A. FEO
Keyword(s):  
Continuum Limit ◽  
Yang Mills ◽  
The Continuum ◽  
Super Yang Mills Theory

scholarly journals Large N scaling and factorization in SU(N) Yang-Mills theory

2018 ◽  
Vol 175 ◽  
pp. 11018 ◽  
Author(s):  
Miguel García Vera ◽  
Rainer Sommer
Keyword(s):  
Lattice Spacing ◽  
Continuum Limit ◽  
Finite Lattice ◽  
Gradient Flow ◽  
Scaling Up ◽  
Wilson Loops ◽  
Yang Mills ◽  
Large N ◽  
The Continuum

We present results for Wilson loops smoothed with the Yang-Mills gradient flow and matched through the scale t0. They provide renormalized and precise operators allowing to test the 1/N2 scaling both at finite lattice spacing and in the continuum limit. Our results show an excellent scaling up to 1/N = 1/3. Additionally, we obtain a very precise non-perturbative confirmation of factorization in the large N limit.

MATRIX REGULARIZATION OF N = 4 SYM ON R × S3

2008 ◽  
Vol 23 (14n15) ◽  
pp. 2199-2200 ◽  
Author(s):  
GORO ISHIKI
Keyword(s):  
Gauge Symmetry ◽  
Plane Wave ◽  
Regularization Method ◽  
Ward Identity ◽  
Continuum Limit ◽  
Beta Function ◽  
Yang Mills ◽  
Planar Limit ◽  
Matrix Regularization ◽  
The Continuum

We revealed a relationship between the plane wave matrix model (PWMM) and N =4 super Yang-Mills (SYM) theory on R × S3: N =4 SYM on R × S3 is equivalent to the theory around a certain vacuum of PWMM. It is suggested from this relation that N =4 SYM on R × S3 is regularized by PWMM in the planar limit. Because PWMM originally possesses the gauge symmetry and SU(2|4) symmetry, this regularization also preserves these symmetries. In order to check the validity of this matrix regularization method, we calculate the Ward identity and the beta function at the 1-loop level. We find that the Ward identity is satisfied and the beta function vanishes in the continuum limit. The former result is consistent with the gauge symmetry of PWMM. The latter suggests the possibility that the conformal symmety is restored in the continuum limit.

scholarly journals Supermultiplets of the N=1 supersymmetric Yang-Mills theory in the continuum limit

2016 ◽  
Author(s):  
Pietro Giudice ◽  
Georg Bergner ◽  
Istvan Montvay ◽  
Gernot Münster ◽  
Stefano Piemonte
Keyword(s):  
Continuum Limit ◽  
Yang Mills ◽  
The Continuum

scholarly journals LATTICE FORMULATION OF SUPERSYMMETRIC YANG–MILLS THEORIES WITHOUT FINE TUNING

1998 ◽  
Vol 13 (16) ◽  
pp. 2841-2855 ◽  
Author(s):  
NOBUHITO MARU ◽  
JUN NISHIMURA
Keyword(s):  
Dimensional Reduction ◽  
Continuum Limit ◽  
Three Dimensions ◽  
Fine Tuning ◽  
Majorana Fermion ◽  
Dirac Fermion ◽  
Two Dimensional ◽  
Yang Mills ◽  
Gauge Anomaly ◽  
The Continuum

We consider an application of the overlap formalism to supersymmetric Yang–Mills theory in three dimensions. We extend the overlap formalism for 3D Dirac fermion to Majorana fermion and show that the parity invariance is exactly preserved, which ensures that the continuum limit is supersymmetric without fine tuning. For SU (N) gauge group, N must be taken to be even in order to make the theory free from global gauge anomaly. We also discuss how to obtain two-dimensional super Yang–Mills theory from the 3D theory through dimensional reduction on the lattice.

scholarly journals Is N = 2 Large?

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Ryuichiro Kitano ◽  
Norikazu Yamada ◽  
Masahito Yamazaki
Keyword(s):  
Continuum Limit ◽  
Vacuum Energy ◽  
Spontaneous Breaking ◽  
Topological Information ◽  
Quantitative Evidence ◽  
Yang Mills ◽  
Topological Excitations ◽  
Dimensionless Coefficient ◽  
Cp Symmetry ◽  
The Continuum

Abstract We study θ dependence of the vacuum energy for the 4d SU(2) pure Yang-Mills theory by lattice numerical simulations. The response of topological excitations to the smearing procedure is investigated in detail, in order to extract topological information from smeared gauge configurations. We determine the first two coefficients in the θ expansion of the vacuum energy, the topological susceptibility χ and the first dimensionless coefficient b2, in the continuum limit. We find consistency of the SU(2) results with the large N scaling. By analytic continuing the number of colors, N , to non-integer values, we infer the phase diagram of the vacuum structure of SU(N) gauge theory as a function of N and θ. Based on the numerical results, we provide quantitative evidence that 4d SU(2) Yang-Mills theory at θ = π is gapped with spontaneous breaking of the CP symmetry.

scholarly journals Ergodic sampling of the topological charge using the density of states

2021 ◽  
Vol 81 (4) ◽  
Author(s):  
Guido Cossu ◽  
David Lancaster ◽  
Biagio Lucini ◽  
Roberto Pellegrini ◽  
Antonio Rago
Keyword(s):  
Density Of States ◽  
Topological Charge ◽  
Lattice Spacing ◽  
Continuum Limit ◽  
Scaling Properties ◽  
Yang Mills ◽  
Autocorrelation Time ◽  
Firm Evidence ◽  
Sizeable Reduction ◽  
The Continuum

AbstractIn lattice calculations, the approach to the continuum limit is hindered by the severe freezing of the topological charge, which prevents ergodic sampling in configuration space. In order to significantly reduce the autocorrelation time of the topological charge, we develop a density of states approach with a smooth constraint and use it to study SU(3) pure Yang Mills gauge theory near the continuum limit. Our algorithm relies on simulated tempering across a range of couplings, which guarantees the decorrelation of the topological charge and ergodic sampling of topological sectors. Particular emphasis is placed on testing the accuracy, efficiency and scaling properties of the method. In their most conservative interpretation, our results provide firm evidence of a sizeable reduction of the exponent z related to the growth of the autocorrelation time as a function of the inverse lattice spacing.

Instability and Collapse in Discrete Wave Equations

2005 ◽  
Vol 5 (3) ◽  
pp. 223-241
Author(s):  
A. Carpio ◽  
G. Duro
Keyword(s):  
Continuum Limit ◽  
Wave Equations ◽  
Numerical Solutions ◽  
Blow Up ◽  
Theoretical Predictions ◽  
Initial States ◽  
The Impact ◽  
The Continuum

AbstractUnstable growth phenomena in spatially discrete wave equations are studied. We characterize sets of initial states leading to instability and collapse and obtain analytical predictions for the blow-up time. The theoretical predictions are con- trasted with the numerical solutions computed by a variety of schemes. The behavior of the systems in the continuum limit and the impact of discreteness and friction are discussed.

scholarly journals Super Yang-Mills theories with inhomogeneous mass deformations

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Yoonbai Kim ◽  
O-Kab Kwon ◽  
D. D. Tolla
Keyword(s):  
Boundary Condition ◽  
Killing Spinor ◽  
Vacuum Equation ◽  
Constant Mass ◽  
Yang Mills ◽  
Spatial Coordinate ◽  
Mass Functions ◽  
Vacuum Solutions ◽  
Super Yang Mills Theory

Abstract We construct the 4-dimensional $$ \mathcal{N}=\frac{1}{2} $$ N = 1 2 and $$ \mathcal{N} $$ N = 1 inhomogeneously mass-deformed super Yang-Mills theories from the $$ \mathcal{N} $$ N = 1* and $$ \mathcal{N} $$ N = 2* theories, respectively, and analyse their supersymmetric vacua. The inhomogeneity is attributed to the dependence of background fluxes in the type IIB supergravity on a single spatial coordinate. This gives rise to inhomogeneous mass functions in the $$ \mathcal{N} $$ N = 4 super Yang-Mills theory which describes the dynamics of D3-branes. The Killing spinor equations for those inhomogeneous theories lead to the supersymmetric vacuum equation and a boundary condition. We investigate two types of solutions in the $$ \mathcal{N}=\frac{1}{2} $$ N = 1 2 theory, corresponding to the cases of asymptotically constant mass functions and periodic mass functions. For the former case, the boundary condition gives a relation between the parameters of two possibly distinct vacua at the asymptotic boundaries. Brane interpretations for corresponding vacuum solutions in type IIB supergravity are also discussed. For the latter case, we obtain explicit forms of the periodic vacuum solutions.

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.

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