Rationality of vertex operator algebra V_L^+: higher rank

TL;DR

This paper proves that the fixed point vertex operator algebra V_L^+ derived from a positive definite even lattice lattice is rational, extending understanding of its algebraic structure.

Contribution

It establishes the rationality of V_L^+ for higher rank lattices, a significant step in vertex operator algebra theory.

Findings

V_L^+ is rational for positive definite even lattices.

The automorphism of order 2 plays a key role in the structure.

Results extend previous work to higher rank lattices.

Abstract

The lattice vertex operator V_L associated to a positive definite even lattice L has an automorphism of order 2 lifted from -1 isometry of L. It is established that the fixed point vertex operator algebra V_L^+ is rational.