Nekrasov and Argyres-Douglas theories in spherical Hecke algebra representation
arXiv:1608.05027 · doi:10.1016/j.nuclphysb.2017.03.012
Abstract
AGT conjecture connects Nekrasov instanton partition function of 4D quiver gauge theory with 2D Liouville conformal blocks. We re-investigate this connection using the central extension of spherical Hecke algebra in q-coordinate representation, q being the instanton expansion parameter. Based on AFLT basis together with interwiners we construct gauge conformal state and demonstrate its equivalence to the Liouville conformal state, with careful attention to the proper scaling behavior of the state. Using the colliding limit of regular states, we obtain the formal expression of irregular conformal states corresponding to Argyres-Douglas theory, which involves summation of functions over Young diagrams.
22 pages; v2: minor modifications, published version
References in corpus (5)
- A_{N-1} conformal Toda field theory correlation functions from conformal N=2 SU(N) quiver gauge theories
- Asymptotically free N=2 theories and irregular conformal blocks
- Virasoro constraint for Nekrasov instanton partition function
- Virasoro irregular conformal block and beta deformed random matrix model
- Spherical Hecke algebra in the Nekrasov-Shatashvili limit