Analytical Traces on Coulomb Branches of Quiver Gauge Theories

TL;DR

This paper constructs explicit twisted traces for quantum Coulomb branches of conical theories, linking algebraic structures to conformal field theory correlation functions and advancing mathematical understanding of these quantum spaces.

Contribution

It introduces an operator representation of Coulomb branch algebras and derives integral formulas for twisted traces, providing a new explicit realization.

Findings

Explicit construction of twisted traces for Coulomb branches

Integral formulas linking algebra to conformal field theory

Enhanced mathematical understanding of quantum Coulomb branches

Abstract

In this paper, we present an explicit construction of twisted traces for quantum Coulomb branches of conical theories. We develop an operator representation of the Coulomb branch algebra and use it to derive integral formulas for the twisted trace. Our construction provides a concrete realization of twisted traces that arise as the correlation functions of a conformal field theory, particularly in the work of Beem, Peelaers, and Rastelli. This complements recent developments in the study of twisted traces on quantum Higgs branches and offers new mathematical insights into the structure of quantum Coulomb branches.