3D N = 1 SYM Chern-Simons theory on the Lattice

TL;DR

This paper develops a lattice implementation for 3D N=1 supersymmetric Yang-Mills theory with Chern-Simons term, highlighting challenges like the sign problem and anomalies at nonzero Chern-Simons number.

Contribution

It introduces a novel lattice method for simulating 3D N=1 SUSY Yang-Mills with Chern-Simons term, addressing the implementation and associated sign problem.

Findings

Implementation of the Chern-Simons term on the lattice.

Identification of a sign problem at nonzero Chern-Simons number.

Demonstration of the vanishing partition function at zero Chern-Simons number.

Abstract

We present a method to implement 3-dimensional N = 1 SUSY Yang-Mills theory (a theory with two real supercharges containing gauge fields and an adjoint Majorana fermion) on the lattice, including a way to implement the Chern-Simons term present in this theory. At nonzero Chern-Simons number our implementation suffers from a sign problem which will make the numerical effort grow exponentially with volume. We also show that the theory with vanishing Chern-Simons number is anomalous; its partition function identically vanishes.