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Affine SL(2) conformal blocks from 4d gauge theories

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arxiv 1005.4469 v2 pith:EYVEYSCV submitted 2010-05-25 hep-th math.AGmath.RT

Affine SL(2) conformal blocks from 4d gauge theories

classification hep-th math.AGmath.RT
keywords blocksconformalgaugetheoriesaffineinstantonorderresults
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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We study Nekrasov's instanton partition function of four-dimensional N=2 gauge theories in the presence of surface operators. This can be computed order by order in the instanton expansion by using results available in the mathematical literature. Focusing in the case of SU(2) quiver gauge theories, we find that the results agree with a modified version of the conformal blocks of affine SL(2) Lie algebra. These conformal blocks provide, in the critical limit, the eigenfunctions of the corresponding quantized Hitchin Hamiltonians.

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Cited by 3 Pith papers

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    Generalized Schur indices of N=2 class S theories are expressed using eigenfunctions of non-relativistic elliptic Calogero-Moser models, with extensions claimed for N=1 SCFTs via limits of models like Inozemtsev.

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