VOAs generated by two conformal vectors whose $\tau$-involutions generate $S_3$

Abstract

We determined the inner products of two conformal vectors with central charge 1/2 whose τ-involutions generates S_3 if none of τ-involutions are trivial. We also see that a subVA generated by such conformal vectors is a VOA with central charge 1/2+20/21 or $4/5+6/7 and has a Griess algebra of dimension three or four, respectively.

19 pages, Latex, corrected some comment