Five dimensional gauge theories and vertex operators

TL;DR

This paper explores five-dimensional supersymmetric gauge theories and their connection to q-deformed conformal field theories, revealing how matter hypermultiplets correspond to vertex operators and generalizing previous K-theory results.

Contribution

It introduces a novel link between 5D gauge theories, K-theory, and q-deformed CFTs, extending prior work to include matter hypermultiplets via vertex operators.

Findings

Coupling to hypermultiplets inserts specific vertex operators.

Partition functions relate to correlation functions in q-deformed CFT.

Generalization of previous K-theory results to include matter fields.

Abstract

We study supersymmetric gauge theories in five dimensions, using their relation to the K-theory of the moduli spaces of torsion free sheaves. In the spirit of the BPS/CFT correspondence the partition function and the expectation values of the chiral, BPS protected observables are given by the matrix elements and more generally by the correlation functions in some q-deformed conformal field theory in two dimensions. We show that the coupling of the gauge theory to the bi-fundamental matter hypermultiplet inserts a particular vertex operator in this theory. In this way we get a generalization of the main result of \cite{CO} to $K$-theory. The theory of interpolating Macdonald polynomials is an important tool in our construction.