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arXiv · 1602.02772

VEV of Baxter's Q-operator in N=2 gauge theory and the BPZ differential equation

Gabriel Poghosyan·Rubik Poghossian
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Abstract

In this short notes using AGT correspondence we express simplest fully degenerate primary fields of Toda field theory in terms an analogue of Baxter's $Q$-operator naturally emerging in ${\cal N}=2$ gauge theory side. This quantity can be considered as a generating function of simple trace chiral operators constructed from the scalars of the ${\cal N}=2$ vector multiplets. In the special case of Liouville theory, exploring the second order differential equation satisfied by conformal blocks including a degenerate at the second level primary field (BPZ equation) we derive a mixed difference-differential relation for $Q$-operator. Thus we generalize the $T$-$Q$ difference equation known in Nekrasov-Shatashvili limit of the $Ω$-background to the generic case.

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Gabriel Poghosyan, Rubik Poghossian. 2016-02-08. VEV of Baxter's Q-operator in N=2 gauge theory and the BPZ differential equation. https://doi.org/10.1007/jhep11(2016)058

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