Year: 2019
Type: article
Abstract: We define and study a class of $$ \mathcal{N} $$ N = 2 vertex operator algebras $$ {\mathcal{W}}_{\mathrm{G}} $$ W G labelled by complex reflection groups. They are extensions of the $$ \mathcal{N} $$ 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 $$ \mathcal{N} $$ N = 2 super Virasoro algebra enhances to the (small) $$ \mathcal{N} $$ N = 4 superconformal algebra. With the exception of G = ℤ2, which corresponds to just the $$ \mathcal{N} $$ 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 $$ {\mathcal{W}}_{\mathrm{G}} $$ W G in terms of rank(G) βγbc ghost systems, generalizing a construction of Adamovic for the $$ \mathcal{N} $$ N = 4 algebra at c = −9. If G is a Weyl group, $$ {\mathcal{W}}_{\mathrm{G}} $$ W G is believed to coincide with the $$ \mathcal{N} $$ 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, $$ {\mathcal{W}}_{\mathrm{G}} $$ W G is conjecturally associated to an $$ \mathcal{N} $$ N = 3 4d superconformal field theory. The free-field realization allows to determine the elusive “R-filtration” of $$ {\mathcal{W}}_{\mathrm{G}} $$ W G , and thus to recover the full Macdonald index of the parent 4d theory.
Source: Journal of High Energy Physics
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
Awards: Theoretical Physics, G4045239135
OpenAlex ID: W2897105175