A different approach to positive traces on generalized q-Weyl algebras

TL;DR

This paper explores positive twisted traces on generalized q-Weyl algebras, demonstrating uniqueness in cases related to four-dimensional gauge theories, which could impact computations in superconformal field theories.

Contribution

It extends previous work by considering more general automorphisms, showing the uniqueness of positive traces for those related to Schur indices in gauge theories.

Findings

Positive twisted traces are unique for automorphisms corresponding to Schur indices.

Generalization from specific q-Weyl algebra cases to broader automorphisms.

Potential applications in superconformal field theory computations.

Abstract

Positive twisted traces are mathematical objects that could be useful in computing certain parameters of superconformal field theories. The case when $\mathcal{A}$ is a $q$-Weyl algebra and $\rho$ is a certain antilinear automorphism of $\mathcal{A}$ was considered in arXiv:2105.12652. Here we consider more general choices of $\rho$. In particular, we show that for $\rho$ corresponding to a standard Schur index of a four-dimensional gauge theory a positive trace is unique.