English

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

High Energy Physics - Lattice 2008-11-26 v2 High Energy Physics - Theory

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.

Keywords

Cite

@article{arxiv.0708.3214,
  title  = {3D N = 1 SYM Chern-Simons theory on the Lattice},
  author = {Joshua W. Elliott and Guy D. Moore},
  journal= {arXiv preprint arXiv:0708.3214},
  year   = {2008}
}

Comments

v2, minor changes: expanded discussion in section III c, typos corrected, 17 pages, 9 figures

R2 v1 2026-06-21T09:10:05.871Z