2011/02/28 by A. Belavin, A. A. Belavin, V. Belavin · 1 citation
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Nonlinear Waves and Solitons #hep-th
paper · pdf · doi:10.1016/j.nuclphysb.2011.04.014
published as Nucl.Phys.B850:199-213,2011 · 16 pages, added references, corrected typos
arxiv created 2011/03/07 · openalex publication_date 2011/04/30 · arxiv updated 2011/06/13 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
AGT correspondence gives an explicit expressions for the conformal blocks of d=2 conformal field theory. Recently an explanation of this representation inside the CFT framework was given through the assumption about the existence of the special orthogonal basis in the module of algebra A=Vir\otimesH. The basis vectors are the eigenvectors of the infinite set of commuting integrals of motion. It was also proven that some of these vectors take form of Jack polynomials. In this note we conjecture and verify by explicit computations that in the case of the Virasoro central charge c=1 all basis vectors are just the products of two Jack polynomials. Each of the commuting integrals of motion becomes the sum of two integrals of motion of two noninteracting Calogero models. We also show that in the case c≠1 it is necessary to use two different Feigin-Fuks bosonizations of the Virasoro algebra for the construction of all basis vectors which take form of one Jack polynomial.