Progress and prospects of lattice supersymmetry

TL;DR

This paper reviews recent progress in lattice supersymmetry, highlighting advances in supersymmetric Yang--Mills theories in various dimensions, while discussing ongoing challenges like sign problems and future directions.

Contribution

It provides a concise overview of notable developments in lattice supersymmetry, emphasizing specific theories and identifying key challenges for future research.

Findings

Progress in lattice studies of supersymmetric Yang--Mills theories in lower dimensions.

Advances in understanding N=1 and N=4 supersymmetric theories in four dimensions.

Identification of sign problems as a major obstacle for future work.

Abstract

Supersymmetry plays prominent roles in the study of quantum field theory and in many proposals for potential new physics beyond the standard model, while lattice field theory provides a non-perturbative regularization suitable for strongly interacting systems. Lattice investigations of supersymmetric field theories are currently making significant progress, though many challenges remain to be overcome. In this brief overview I discuss particularly notable progress in three areas: supersymmetric Yang--Mills (SYM) theories in fewer than four dimensions, as well as both minimal N=1 SYM and maximal N=4 SYM in four dimensions. I also highlight super-QCD and sign problems as prominent challenges that will be important to address in future work.