Exact Results in Discretized Gauge Theories

Abstract

We apply the localization technique to topologically twisted N=(2,2) supersymmetric gauge theory on a discretized Riemann surface (the generalized Sugino model). We exactly evaluate the partition function and the vacuum expectation value (vev) of a specific Q-closed operator. We show that both the partition function and the vev of the operator depend only on the Euler characteristic and the area of the discretized Riemann surface and are independent of the detail of the discretization. This localization technique may not only simplify numerical analysis of the supersymmetric lattice models but also connect the well-defined equivariant localization to the empirical supersymmetric localization.

26 pages, 1 figure, references added, typos corrected

References in corpus (10)

• Restoration of supersymmetry on the lattice: Two-dimensional $\mathcal{N}=(2,2)$ supersymmetric Yang-Mills theory
• Observing dynamical supersymmetry breaking with euclidean lattice simulations
• Lattice study of two-dimensional N=(2,2) super Yang-Mills at large-N
• Euclidean lattice simulation for the dynamical supersymmetry breaking
• Lattice Formulation of Two-Dimensional N=(2,2) SQCD with Exact Supersymmetry
• Exact Results in Quiver Quantum Mechanics and BPS Bound State Counting
• Lattice Formulation of Two Dimensional Topological Field Theory
• Two-dimensional N=(2,2) super Yang-Mills theory on computer
• Topologically Twisted $N=(2,2)$ Supersymmetric Yang-Mills Theory on Arbitrary Discretized Riemann Surface
• A Lattice Formulation of Two Dimensional Topological Field Theory

Cited by in corpus (2)

• Anomaly and Sign problem in $\mathcal{N}=(2,2)$ SYM on Polyhedra : Numerical Analysis
• Kazakov-Migdal model on the Graph and Ihara Zeta Function