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

Understand

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.