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 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.

scholarly journals Truncation of lattice N = 4 super Yang-Mills

2018 ◽  
Vol 175 ◽  
pp. 11008 ◽  
Author(s):  
Joel Giedt ◽  
Simon Catterall ◽  
Raghav Govind Jha
Keyword(s):  
Gauge Theory ◽  
Gauge Symmetry ◽  
Moduli Space ◽  
Lattice Spacing ◽  
Continuum Limit ◽  
Power Counting ◽  
Yang Mills ◽  
Free Theory ◽  
Lattice Gauge ◽  
Two Sectors

In twisted and orbifold formulations of lattice N = 4 super Yang-Mills, the gauge group is necessarily U(1) × SU(N), in order to be consistent with the exact scalar supersymmetry Q. In the classical continuum limit of the theory, where one expands the link fields around a point in the moduli space and sends the lattice spacing to zero, the diagonal U(1) modes decouple from the SU(N) sector, and give an uninteresting free theory. However, lattice artifacts (described by irrelevant operators according to naive power-counting) couple the two sectors, so removing the U(1) modes is a delicate issue. We describe how this truncation to an SU(N) gauge theory can be obtained in a systematic way, with violations of Q that fall off as powers of 1=N2. We are able to achieve this while retaining exact SU(N) lattice gauge symmetry at all N, and provide both theoretical arguments and numerical evidence for the 1=N2 suppression of Q violation.

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 CHIRAL GAUGE THEORIES ON THE LATTICE WITHOUT GAUGE FIXING?

1994 ◽  
Vol 05 (02) ◽  
pp. 327-329
Author(s):  
WOLFGANG BOCK
Keyword(s):  
Gauge Theory ◽  
Gauge Symmetry ◽  
Symmetry Breaking ◽  
Continuum Limit ◽  
Gauge Theories ◽  
Gauge Fixing ◽  
The Continuum

We discuss two proposals for a non-perturbative formulation of chiral gauge theories on the lattice. In both cases gauge symmetry is broken by the regularization. We aim at a dynamical restoration of symmetry. If the gauge symmetry breaking is not too severe this procedure could lead in the continuum limit to the desired chiral gauge theory.

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.

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