Some Twisted Sectors for the Moonshine Module

The construction of twisted sectors, or g-twisted modules, for a vertex operator algebra V and automorphism g, is a fundamental problem in algebraic conformal field theory and the theory of orbifold models. For the moonshine module V , whose automorphism is the Monster M, Tuite has shown that this problem is intimately related to the generalized moonshine conjecture which relates hauptmoduln to twisted sectors. In this paper we show how to give a uniform existence proof for irreducible gtwisted V -modules for elements of type 2A, 2B and 4A in M. The most interesting of these is the twisted sector V (2A), whose automorphism group is essentially the centralizer of 2A in M. This is a 2-fold central extension of the Baby Monster, the second largest sporadic simple group. We also establish uniqueness of the twisted sectors and the hauptmodul property for the graded traces of automorphisms of odd order, as predicted by conformal field theory.