Lattice Supersymmetric Field Theories, Summer 2022
Lattice field theory provides a non-perturbative regularization suitable for strongly interacting systems, which has proven crucial to the study of quantum chromodynamics among many other theories. Lattice investigations of supersymmetric field theories have a long history but often struggle due to the interplay of supersymmetry with the lattice discretization of space-time. This short course reviews these issues and recent progress overcoming them, as part of the August 2022 program Nonperturbative and Numerical Approaches to Quantum Gravity, String Theory, and Holography at the International Centre for Theoretical Sciences in Bengaluru.
Part 1 (22 August): Recording and slides
Motivations for lattice supersymmetry; Supersymmetry breaking in discrete space-time; Twisting continuum N=4 super-Yang–Mills (SYM); Discretizing twisted N=4 SYM
Part 2 (24 August): Recording and slides
Lattice N=4 SYM; Continuum limit via renormalization group, semi-classical analysis and lattice perturbation theory; Regulating SU(N) and U(1) flat directions to carry out numerical computations; Improved action and public code
Part 3 (25 August): Recording and slides
Lattice N=4 static potential and Coulomb coefficient; 2d N=(8,8) thermodynamics and holography; 4d N=1 SYM with Wilson-type and chiral lattice fermions; Super-QCD and sign problems as future frontiers
Supersymmetric lattice field theories remain a specialized topic for which the best resources are review articles that briefly summarize the research literature and place it into context.
- I wrote the most recent (brief) review: Lattice studies of supersymmetric gauge theories (2022)
- The most detailed review remains Exact lattice supersymmetry by Simon Catterall, David Kaplan and Mithat Unsal (2009)
Last modified 29 August 2022