2000/04/10 by BL Feigin, Feigin, BL, AM Semikhatov +3 · 1 citation
Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #hep-th
paper · pdf · doi:10.48550/arxiv.hep-th/0004066
LaTeX2e: amsart++, 54pp. V2: some changes in the presentation, references added
arxiv created 2001/04/01 · arxiv updated 2009/11/30
We show that each unitary representation of the N=2 superVirasoro algebra can be realized in terms of ``collective excitations'' over a filled Dirac sea of fermionic operators satisfying a generalized exclusion principle. These are semi-infinite forms in the modes of one of the fermionic currents. The constraints imposed on the fermionic operators have a counterpart in the form of a model one-dimensional lattice system, studying which allows us to prove the existence of a remarkable monomial basis in the semi-infinite space. This leads to a Rogers--Ramanujan-like character formula. We construct the N=2 action on the semi-infinite space using a filtration by finite-dimensional subspaces (the structure of which is related to the supernomial coefficients); the main technical tool is provided by the dual functional realization. As an application, we identify the coinvariants with the dual to a space of meromorphic functions on products of punctured Riemann surfaces with a prescribed behaviour on multiple diagonals. For products of punctured CP1, such spaces are related to the unitary N=2 fusion algebra, for which we also give an independent derivation.