PIRSA:14100066 Scientific Series

DOI10.48660/14100066

Series: Quantum Fields and Strings

Nekrasov, N. (2014). QQ-CHARACTERS, GAUGE THEORY and non-perturbative Dyson-Schwinger equations. Perimeter Institute. https://pirsa.org/14100066

Nekrasov, Nikita. QQ-CHARACTERS, GAUGE THEORY and non-perturbative Dyson-Schwinger equations. Perimeter Institute, Oct. 14, 2014, https://pirsa.org/14100066 

@misc{ pirsa_PIRSA:14100066,
  doi = {10.48660/14100066},
  url = {https://pirsa.org/14100066},
  author = {Nekrasov, Nikita},
  keywords = {},
  language = {en},
  title = {QQ-CHARACTERS, GAUGE THEORY and non-perturbative Dyson-Schwinger equations},
  publisher = {Perimeter Institute},
  year = {2014},
  month = {oct},
  note = {PIRSA:14100066 see, \url{https://pirsa.org}}
}

Abstract

We report on recent advances in understanding the non-local symmetries of quantum field theory, notably gauge theory. The symmetries relate topologically distinct sectors of the field space. We study these symmetries in some detail in the context of the BPS/CFT correspondence. We also introduce a notion of qq-characters, which generalize the q-characters of quantum affine algebras, introduced by E. Frenkel and N. Reshetikhin, and conjecturally are related to the (q, t)-characters introduced by H. Nakajima. We show that the qq-characters can be used to derive an infinite set of Dyson-Schwinger type relations which imply that the supersymmetric partition functions of four dimensional gauge theory (with surface operators) obey BPZ and KZB-type equations.

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