Lattice study of two-dimensionalN=(2,2)super Yang-Mills theory at largeN

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 = ∞. 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. *

Monte Carlo approach to the string/M-theory

“…This exact supersymmetry, combined with other global symmetries, assures the correct continuum limit. It was first argued at perturbative level [11] [12,13,14,15] and then confirmed nonperturbatively by the Monte-Carlo simulation [16,17,18].…”

A method for measuring the Witten index using lattice simulation

“…[20,21]. The large-N property of 2-dimensional N = (2, 2) system has been studied with the same motivation [22], although this system has smaller number of supersymmetries.…”

What lattice theorists can do for superstring/M-theory

“…In higher dimensions, the exact symmetries are not powerful enough to exclude possible fine tunings. 2d N = (2, 2) SYM, which is the dimensional reduction of 4d N = 1 SYM, has been studied numerically [85][86][87] and the validity of the regularizations at nonperturbative level has been confirmed. 2d N = (8, 8) SYM, which is dual to the D1-brane theory, has also been studied.…”