A Characetrization of Vertex Operator Algebra L(1/2,0)\otimes L(1/2,0)

TL;DR

This paper characterizes a specific class of vertex operator algebras with central charge 1, showing they are isomorphic to a tensor product of two minimal models under certain conditions.

Contribution

It provides a classification result for vertex operator algebras with particular properties, identifying them as a specific tensor product of minimal models.

Findings

Any such VOA with the given properties is isomorphic to L(1/2,0)⊗L(1/2,0)

The dimension of the weight 2 subspace is at least 2

The VOA is uniquely determined by the specified conditions

Abstract

It is shown that any simple, rational and C_2-cofinite vertex operator algebra whose weight 1 subspace is zero, the dimension of weight 2 subspace is greater than or equal to 2 and with central charge c=1, is isomorphic to L(1/2,0)\otimes L(1/2,0).