The fourth root of the Kogut-Susskind determinant via infinite component fields

TL;DR

This paper explores the theoretical foundations of using the fourth root of the Kogut-Susskind determinant in lattice fermion simulations, framing it within local field theories to assess its validity.

Contribution

It introduces a local field theory interpolation between standard Kogut-Susskind fermions and the fourth root approximation, analyzing conditions for its validity.

Findings

Provides a local field theoretical framework for the fourth root trick.

Identifies conditions under which the approximation is smooth and potentially valid.

Raises questions about the fundamental validity of the fourth root approach.

Abstract

An example of interpolation by means of local field theories between the case of normal Kogut-Susskind fermions and the case of keeping just the fourth root of the Kogut-Susskind determinant is given. For the fourth root trick to be a valid approximation certain limits need to be smooth. The question about the validity of the fourth root trick is not resolved, only cast into a local field theoretical framework.