Large Gauge Ward Identity

TL;DR

This paper investigates the nonlinear Ward identities associated with large gauge invariance in 0+1 dimensional theories, deriving identities for fermions and scalars, and exploring their structure in supersymmetric contexts.

Contribution

It derives and analyzes the nonlinear large gauge Ward identities for simple 0+1 dimensional theories, including supersymmetric cases, highlighting their structure and potential generalizations.

Findings

Ward identities are nonlinear in these theories.

Supersymmetric theories involve infinitely many Fourier modes in solutions.

The structure of Ward identities may differ in higher dimensions.

Abstract

We study the question of the Ward identity for "large" gauge invariance in 0+1 dimensional theories. We derive the relevant Ward identities for a single flavor fermion and a single flavor complex scalar field interacting with an Abelian gauge field. These identities are nonlinear. The Ward identity for any other complicated theory can be derived from these basic sets of identities. However, the structure of the Ward identity changes since these are nonlinear identities. In particular, we work out the "large" gauge Ward identity for a supersymmetric theory involving a single flavor of fermion as well as a complex scalar field. Contrary to the effective action for the individual theories, the solution of the Ward identity in the supersymmetric theory involves an infinity of Fourier component modes. We comment on which features of this analysis are likely/unlikely to generalize to the 2+1 dimensional theory.