2018/10/31 by Federico Bonetti, Carlo Meneghelli, Leonardo Rastelli · 1 citation
Physics and Astronomy · Mathematics · #hep-th #math.QA #math.RT
paper · pdf · doi:10.1007/jhep05(2019)155
70 pages
arxiv created 2019/03/22 · arxiv updated 2019/06/26
We define and study a class of N=2 vertex operator algebras WG labelled by complex reflection groups. They are extensions of the N=2 super Virasoro algebra obtained by introducing additional generators, in correspondence with the invariants of the complex reflection group G. If G is a Coxeter group, the N=2 super Virasoro algebra enhances to the (small) N=4 superconformal algebra. With the exception of G = ℤ2, which corresponds to just the N=4 algebra, these are non-deformable VOAs that exist only for a specific negative value of the central charge. We describe a free-field realization of WG in terms of rank(G) βγbc ghost systems, generalizing a construction of Adamovic for the N=4 algebra at c = -9. If G is a Weyl group, WG is believed to coincide with the N=4 VOA that arises from the four-dimensional super Yang-Mills theory whose gauge algebra has Weyl group G. More generally, if G is a crystallographic complex reflection group, WG is conjecturally associated to an N=3 4d superconformal field theory. The free-field realization allows to determine the elusive `R-filtration' of WG, and thus to recover the full Macdonald index of the parent 4d theory