Abstract
In this short note using AGT correspondence we express the simplest fully degenerate primary fields of Toda field theory in terms of an analogue of Baxter’s Q-operator naturally emerging on the \( \mathcal{N} \) = 2 gauge theory side. This quantity can be considered as a generating function of certain chiral operators constructed from the scalars of the \( \mathcal{N} \) = 2 vector multiplets. In the special case of Liouville theory, exploring the second order differential equation satisfied by conformal blocks including a primary field which is degenerate at the second level (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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Poghosyan, G., Poghossian, R. VEV of Baxter’s Q-operator in N = 2 gauge theory and the BPZ differential equation. J. High Energ. Phys. 2016, 58 (2016). https://doi.org/10.1007/JHEP11(2016)058
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DOI: https://doi.org/10.1007/JHEP11(2016)058