Positive traces on quantized abelian Coulomb branches

TL;DR

This paper classifies positive traces on abelian Coulomb branches, which are important in supersymmetric gauge theories, by analyzing the structure of quantized Coulomb branches with an antilinear automorphism.

Contribution

It provides a complete classification of positive traces on all abelian Coulomb branches, expanding understanding of their algebraic and physical properties.

Findings

Classification of positive traces on abelian Coulomb branches

Identification of conditions for positivity in traces

Connection to supersymmetric gauge theory applications

Abstract

Let $A=A_{G,N}^{\hbar=1}$ be a quantized Coulomb branch with an antilinear automorphism $\rho$. A map $T\colon A\to\mathbb{C}$ is called a positive trace if $T(a\rho(a))>0$ for all nonzero $a\in A$. Positive traces on Coulomb branches appear in the study of supersymmetric gauge theories. We classify positive traces on all abelian Coulomb branches, meaning $G=(\mathbb{C}^{\times})^d$ is a torus.