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VOLUME 90 | ISSUE 11 | PAGE 803
Non-conformal limit of AGT relation from the 1-point torus conformal block
V. Alba^{\star + \nabla\triangle 1)}, And. Morozov^{\star\square}

^{\star}Institute for Theoretical and Experimental Physics, 117218 Moscow, Russia
+Landau Institute for Theoretical Physics RAS, 119334 Moscow, Russia
^\nablaDepartment of General and Applied Physics, Moscow Institute of Physics and Technology
141700 Dolgoprudny, Moscow Reg., Russia
^\squarePhysical Department, Moscow State University, 119991 Moscow, Russia
^\triangleBogolyubov Institute for Theoretical Physics of the National Academy of Sciences of Ukraine
03680 Kyiv, Ukraine

PACS: 11.15.-q, 11.25.Hf
Given a 4d \mathcal{N}=2 SYM theory, one can construct the Seiberg-Witten prepotentional, which involves a sum over instantons. Integrals over instanton moduli spaces require regularisation. For UV-finite 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 WN<sub>c</sub> chiral algebra (virasoro algebra in our case). For Nc=2 and one adjoint multiplet it coincides with a torus 1-point 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 \mathcal{N}=2 super symmetric Yang-Mills theory. Though technically more involved, the limit is the same as in the case of fundamental multiplets, and this provides one more non-trivial check of AGT conjecture.

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