Lattice studies of supersymmetric gauge theories

TL;DR

This review summarizes recent advances in lattice studies of supersymmetric gauge theories, highlighting progress in lower-dimensional SYM theories, N=1 and N=4 SYM in four dimensions, and discussing key challenges like sign problems.

Contribution

It provides a comprehensive overview of recent lattice investigations into supersymmetric gauge theories, emphasizing new results and ongoing challenges.

Findings

Progress in lattice simulations of lower-dimensional SYM theories

Initial results on N=1 and N=4 supersymmetric Yang--Mills theories

Identification of sign problems as major obstacles for future research

Abstract

Supersymmetry plays prominent roles in the study of quantum field theory and in many proposals for potential new physics beyond the standard model. Lattice field theory provides a non-perturbative regularization suitable for strongly interacting systems. This invited review briefly summarizes significant recent progress in lattice investigations of supersymmetric field theories, as well as some of the challenges that remain to be overcome. I focus on progress in three areas: supersymmetric Yang--Mills (SYM) theories in fewer than four space-time dimensions, as well as both minimal N=1 SYM and maximal N=4 SYM in four dimensions. I also highlight superQCD and sign problems as prominent challenges that will be important to address in future work.