Non-conformal limit of AGT relation from the 1-point torus conformal block

Abstract

Given a 4d N=2 SUSY gauge theory, one can construct the Seiberg-Witten\nprepotentional, which involves a sum over instantons. Integrals over instanton\nmoduli spaces require regularisation. For UV-finite theories the AGT conjecture\nfavours particular, Nekrasov's way of regularization. It implies that\nNekrasov's partition function equals conformal blocks in 2d theories with\nW_{N_c} chiral algebra. For $N_c=2$ and one adjoint multiplet it coincides with\na torus 1-point Virasoro conformal block. We check the AGT relation between\nconformal dimension and adjoint multiplet's mass in this case and investigate\nthe limit of the conformal block, which corresponds to the large mass limit of\nthe 4d theory e.i. the asymptotically free 4d N=2 supersymmetric Yang-Mills\ntheory. Though technically more involved, the limit is the same as in the case\nof fundamental multiplets, and this provides one more non-trivial check of AGT\nconjecture.\n