Deconstruction and other approaches to supersymmetric lattice field theories

TL;DR

This paper reviews recent methods for constructing supersymmetric lattice field theories, introduces new insights into the deconstruction approach, and discusses the complex phase problem related to fermion determinants and their impact on the continuum limit.

Contribution

It provides a comprehensive review of supersymmetric lattice theories and presents new results on the deconstruction approach, clarifying the origin of the complex phase problem and its implications.

Findings

Derivative interactions cause the complex phase problem in fermion determinants.

Irrelevant operators break self-conjugacy of the fermion action in the lattice.

Fermion determinant suppression supports the continuum limit of the theories.

Abstract

This report contains both a review of recent approaches to supersymmetric lattice field theories and some new results on the deconstruction approach. The essential reason for the complex phase problem of the fermion determinant is shown to be derivative interactions that are not present in the continuum. These irrelevant operators violate the self-conjugacy of the fermion action that is present in the continuum. It is explained why this complex phase problem does not disappear in the continuum limit. The fermion determinant suppression of various branches of the classical moduli space is explored, and found to be supportive of previous claims regarding the continuum limit.