Twisted Supersymmetric Gauge Theories and Orbifold Lattices

TL;DR

This paper explores the connection between twisted supersymmetric gauge theories and orbifold lattice formulations, demonstrating how continuum limits of orbifold lattices reproduce known twists in supersymmetric theories.

Contribution

It establishes a detailed relationship between twisted supersymmetric theories and orbifold lattice constructions, including the continuum limit correspondence for $ =4$ SYM.

Findings

Orbifold lattice continuum limit reproduces Marcus twist in $ =4$ SYM.

Lattice supersymmetry corresponds to nilpotent scalar supersymmetry in twisted theories.

Orbifold lattice point group symmetry is a subgroup of the twisted Lorentz group.

Abstract

We examine the relation between twisted versions of the extended supersymmetric gauge theories and supersymmetric orbifold lattices. In particular, for the $\mathcal{N}=4$ SYM in $d=4$, we show that the continuum limit of orbifold lattice reproduces the twist introduced by Marcus, and the examples at lower dimensions are usually Blau-Thompson type. The orbifold lattice point group symmetry is a subgroup of the twisted Lorentz group, and the exact supersymmetry of the lattice is indeed the nilpotent scalar supersymmetry of the twisted versions. We also introduce twisting in terms of spin groups of finite point subgroups of $R$-symmetry and spacetime symmetry.