Positive traces on quantized abelian Coulomb branches

Abstract

Let $A=A_{G,N}^{\hslash =1}$ be a quantized Coulomb branch with an antilinear automorphism $\ddot{I}$. A map $T:A\to \mathbb{C}$ is called a positive trace if $T(a\ddot{I}(a))>0$ 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.

31 pages