On elementary proof of AGT relations from six dimensions

A. Mironov (Institute for Information Transmission Problems, Moscow, 127994, Russia; ITEP, Moscow, 117218, Russia; Lebedev Physics Institute, Moscow, 119991, Russia; National Research Nuclear University MEPhI, Moscow, 115409, 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; Institute of Nuclear Research, Moscow, 117312, Russia; National Research Nuclear University MEPhI, Moscow, 115409, 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.

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      "value": "The actual definition of the Nekrasov functions participating in the AGT relations implies a peculiar choice of contours in the LMNS and Dotsenko\u2013Fateev 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."
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Published on:
05 March 2016
Publisher:
Elsevier
Published in:
Physics Letters B (2016)

DOI:
https://doi.org/10.1016/j.physletb.2016.03.006
Copyrights:
The Authors
Licence:
CC-BY-3.0

Fulltext files: