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On elementary proof of AGT relations from six dimensions

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arxiv 1512.06701 v2 pith:6ATXTZ3D submitted 2015-12-21 hep-th

classification hep-th
keywords relationschoicedimensionselementaryhoweverintegralsactualapplied
verification ladder T0 review T1 audit T2 compute T3 formal
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The actual definition of the Nekrasov functions participating in the AGT relations implies a peculiar choice of contours in the LMNS and Dotsenko-Fateev integrals. Once made explicit and applied to the original triply-deformed (6-dimensional) version of these integrals, this approach reduces the AGT relations to symmetry in q_{1,2,3}, which is just an elementary identity for an appropriate choice of the integration contour (which is, however, a little non-traditional). We illustrate this idea with the simplest example of N=(1,1) U(1) SYM in six dimensions, however, all other cases can be evidently considered in a completely similar way.

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