On elementary proof of AGT relations from six dimensions
A. Mironov (Institute for Information Transmission Problems, Moscow, 127994, Russia, ITEP, Moscow, 117218, Russia, National Research Nuclear University MEPhI, Moscow, 115409, Russia, Lebedev Physics Institute, Moscow, 119991, Russia); A. Morozov (Institute for Information Transmission Problems, Moscow, 127994, Russia, ITEP, Moscow, 117218, Russia, National Research Nuclear University MEPhI, Moscow, 115409, Russia); Y. Zenkevich (ITEP, Moscow, 117218, Russia, National Research Nuclear University MEPhI, Moscow, 115409, Russia, Institute of Nuclear Research, Moscow, 117312, Russia)
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 q1,2,3 , 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.
