Speaker
中塚成徳 (東京大学大学院数理科学研究科)
Date
October 5, 14:45-15:35
Title
Fusion rules of lattice cosets with an application to Feigin-Semikhatov duality (slide)
Abstract
For a vertex operator superalgebra \(V\) and a subalgebra of vertex operator superalgebra \(V_L\) associated with a positive-definite lattice \(L\), we can consider the coset \(C=Com(V_L,V)\). It is well-known that under suitable conditions, the regularity of \(V\) and \(C\) are equivalent. In this case, the Grothendieck rings of their ordinary modules, known as fusion rings, are intimately related to each other. Such examples include rational affine VOAs and parafermion VOAs or the unitary series N=2 superconformal algebra and rational affine VOA associated with \(\mathfrak{sl}_2\).
We prove a concise formula reconstructing the fusion rings from each other in full generality. With this, we not only obtain the above examples but also the fusion rings of rational W-superalgebras associated with \(\mathfrak{sl}_{n|1}\), which generalize the unitary series N=2 superconformal algebra. This is based upon a recent joint work with Thomas Creutzig, Naoki Genra and Ryo Sato.