Lattice study of two-dimensional N=(2,2) super Yang-Mills at large-N

TL;DR

This study uses lattice simulations to explore two-dimensional N=(2,2) super Yang-Mills theory at large N, revealing a bound state with broken symmetry and scalar field clumping, providing insights into non-perturbative dynamics.

Contribution

First lattice simulation of 2D N=(2,2) super Yang-Mills at large N, demonstrating bound state formation and symmetry breaking.

Findings

Existence of a bound state with scalar clumping

Breaking of (Z_N)^2 symmetry in the phase

Results extrapolated to N = infinity

Abstract

We study two-dimensional N=(2,2) SU(N) super Yang-Mills theory on Euclidean two-torus using Sugino's lattice regularization. We perform the Monte-Carlo simulation for N=2,3,4,5 and then extrapolate the result to N = infinity. With the periodic boundary conditions for the fermions along both circles, we establish the existence of a bound state in which scalar fields clump around the origin, in spite of the existence of a classical flat direction. In this phase the global (Z_N)^2 symmetry turns out to be broken. We provide a simple explanation for this fact and discuss its physical implications.