BPS/CFT correspondence: non-perturbative Dyson-Schwinger equations and qq-characters

TL;DR

This paper explores symmetries in quantum field theories with topologically distinct sectors, introducing $qq$-characters to derive Dyson-Schwinger relations that connect supersymmetric partition functions to conformal field theory Ward identities.

Contribution

It introduces $qq$-characters as gauge-invariant observables within the BPS/CFT correspondence to derive non-perturbative Dyson-Schwinger equations.

Findings

Derivation of infinite Dyson-Schwinger-type relations.

Connection of supersymmetric partition functions to 2D conformal field theory Ward identities.

Framework applicable to $ ext{Omega}$-deformed theories with defects.

Abstract

We study symmetries of quantum field theories involving topologically distinct sectors of the field space. To exhibit these symmetries we define special gauge invariant observables, which we call the $qq$-characters. In the context of the BPS/CFT correspondence, using these observables, we derive an infinite set of Dyson-Schwinger-type relations. These relations imply that the supersymmetric partition functions in the presence of $\Omega$-deformation and defects obey the Ward identities of two dimensional conformal field theory and its $q$-deformations. The details will be discussed in the companion papers.