
VOLUME 90 (2009)  ISSUE 11 
PAGE 803

Nonconformal limit of AGT relation from the 1point torus conformal block
V. Alba, And. Morozov
Institute for Theoretical and Experimental Physics, 117218 Moscow, Russia ^{+}Landau Institute for Theoretical Physics RAS, 119334 Moscow, Russia ^{∇}Department of General and Applied Physics, Moscow Institute of Physics and Technology 141700 Dolgoprudny, Moscow Reg., Russia Physical Department, Moscow State University, 119991 Moscow, Russia Bogolyubov Institute for Theoretical Physics of the National Academy of Sciences of Ukraine 03680 Kyiv, Ukraine
PACS: 11.15.q, 11.25.Hf
Abstract
Given a 4d SYM theory, one can construct
the SeibergWitten prepotentional, which involves a sum over instantons.
Integrals over instanton moduli spaces require regularisation. For UVfinite
theories the AGT conjecture favours particular, Nekrasov's way of
regularization. It implies that Nekrasov's partition function equals
conformal blocks in 2d theories with W_{Nc} chiral algebra
(virasoro algebra in our case).
For N_{c}=2 and one adjoint multiplet it coincides with a torus 1point
Virasoro conformal block. We check the AGT relation between conformal
dimension and adjoint multiplet's mass in this case and investigate the large
mass limit of the conformal block, which corresponds to asymptotically free
4d super symmetric YangMills theory. Though technically
more involved, the limit is the same as in the case of fundamental
multiplets, and this provides one more nontrivial check of AGT conjecture.

