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arxiv: 1512.05388 · v2 · submitted 2015-12-16 · ✦ hep-th · math.AC· math.AG· math.QA· math.RT

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

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classification ✦ hep-th math.ACmath.AGmath.QAmath.RT
keywords fieldcorrespondenceobservablesrelationssymmetriescallcharacterscompanion
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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.

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