Anomaly and Sign problem in $\mathcal{N}=(2,2)$ SYM on Polyhedra : Numerical Analysis

Abstract

We investigate the two-dimensional $\mathcal{N}=(2,2)$ supersymmetric Yang-Mills (SYM) theory on the discretized curved space (polyhedra). We first revisit that the number of supersymmetries of the continuum $\mathcal{N}=(2,2)$ SYM theory on any curved manifold can be enhanced at least to two by introducing an appropriate $U(1)$ gauge background associated with the $U(1{)}_V$ symmetry. We then show that the generalized Sugino model on the discretized curved space, which was proposed in our previous work, can be identified to the discretization of this SUSY enhanced theory, where one of the supersymmetries remains and the other is broken but restored in the continuum limit. We find that the $U(1{)}_A$ anomaly exists also in the discretized theory as a result of an unbalance of the number of the fermions proportional to the Euler characteristics of the polyhedra. We then study this model by using the numerical Monte-Carlo simulation. We propose a novel phase-quench method called "anomaly-phase-quenched approximation" with respect to the $U(1{)}_A$ anomaly. We numerically show that the Ward-Takahashi (WT) identity associated with the remaining supersymmetry is realized by adopting this approximation. We figure out the relation between the sign (phase) problem and pseudo-zero-modes of the Dirac operator. We also show that the divergent behavior of the scalar one-point function gets milder as the genus of the background increases. These are the first numerical observations for the supersymmetric lattice model on the curved space with generic topologies.

28 pages, 8 figures, 2 tables. Typos corrected. An equation of WT id and the corresponding numerical result updated. The conclusion is unchanged

References in corpus (39)

• Localization of gauge theory on a four-sphere and supersymmetric Wilson loops
• Exact Results for Wilson Loops in Superconformal Chern-Simons Theories with Matter
• Rigid Supersymmetric Theories in Curved Superspace
• Supersymmetry on a Euclidean Spacetime Lattice I: A Target Theory with Four Supercharges
• Exploring Curved Superspace
• A Euclidean Lattice Construction of Supersymmetric Yang-Mills Theories with Sixteen Supercharges
• A Lattice Formulation of Super Yang-Mills Theories with Exact Supersymmetry
• Supersymmetry on a Euclidean Spacetime Lattice II: Theories with Eight Supercharges
• Super Yang-Mills Theories on the Two-Dimensional Lattice with Exact Supersymmetry
• The RHMC Algorithm for 2 Flavours of Dynamical Staggered Fermions
• Twisted Supersymmetric Gauge Theories and Orbifold Lattices
• Lattice Supersymmetry and Topological Field Theory
• Twisted Superspace on a Lattice
• From Twisted Supersymmetry to Orbifold Lattices
• Various Super Yang-Mills Theories with Exact Supersymmetry on the Lattice
• Restoration of supersymmetry on the lattice: Two-dimensional $\mathcal{N}=(2,2)$ supersymmetric Yang-Mills theory
• Two-Dimensional Compact N=(2,2) Lattice Super Yang-Mills Theory with Exact Supersymmetry
• Observing dynamical supersymmetry breaking with euclidean lattice simulations
• Lattice study of two-dimensional N=(2,2) super Yang-Mills at large-N
• Two-dimensional N=(2,2) super Yang-Mills theory on the lattice via dimensional reduction
• Two-dimensional lattice for four-dimensional N=4 supersymmetric Yang-Mills
• Euclidean lattice simulation for the dynamical supersymmetry breaking
• Absence of sign problem in two-dimensional N=(2,2) super Yang-Mills on lattice
• Relationship between various supersymmetric lattice models
• Lattice formulation of (2,2) supersymmetric gauge theories with matter fields
• Lattice Supersymmetry: Equivalence between the Link Approach and Orbifolding
• Lattice Formulation of Two-Dimensional N=(2,2) SQCD with Exact Supersymmetry
• Two-dimensional N=(2,2) Supersymmetric Lattice Gauge Theory with Matter Fields in the Fundamental Representation
• Relations among Supersymmetric Lattice Gauge Theories via Orbifolding
• Non-perturbative construction of 2D and 4D supersymmetric Yang-Mills theories with 8 supercharges
• Two-dimensional N=(2,2) super Yang-Mills theory on computer
• Ginsparg-Wilson Formulation of 2D N =(2,2) SQCD with Exact Lattice Supersymmetry
• Some physics of the two-dimensional $\mathcal{N}=(2,2)$ supersymmetric Yang-Mills theory: Lattice Monte Carlo study
• Lattice Formulation for 2d N=(2,2), (4,4) Super Yang-Mills Theories without Admissibility Conditions
• Topologically Twisted $N=(2,2)$ Supersymmetric Yang-Mills Theory on Arbitrary Discretized Riemann Surface
• Restoration of supersymmetry in two-dimensional SYM with sixteen supercharges on the lattice
• Lattice formulation of two-dimensional N=(2,2) super Yang-Mills with SU(N) gauge group
• Fermion Actions extracted from Lattice Super Yang-Mills Theories
• Exact Results in Discretized Gauge Theories

Cited by in corpus (8)

• Testing holography using lattice super-Yang--Mills on a 2-torus
• Progress and prospects of lattice supersymmetry
• Lattice studies of supersymmetric gauge theories
• Supersymmetric Gauge Theory on the Graph
• Mass spectrum of $2$-dimensional $\mathcal{N}=(2,2)$ super Yang-Mills theory on the lattice
• Kazakov-Migdal model on the Graph and Ihara Zeta Function
• New conjecture on exact Dirac zero-modes of lattice fermions
• Nonperturbative phase diagram of two-dimensional $\mathcal{N}=(2,2)$ super-Yang--Mills