Integral forms for tensor powers of the Virasoro vertex operator algebra $L(\frac{1}{2},0)$ and their modules

TL;DR

This paper constructs integral forms within tensor powers of the Virasoro vertex operator algebra and its modules, classifies intertwining operators respecting these forms, and explores implications for framed vertex operator algebras.

Contribution

It introduces new integral forms for tensor powers of the Virasoro VOA and their modules, and classifies compatible intertwining operators.

Findings

Constructed integral forms containing the conformal vector in tensor powers of $L(1/2,0)$

Classified intertwining operators that respect these integral forms

Explored potential applications to framed vertex operator algebras

Abstract

We construct integral forms containing the conformal vector $\omega$ in certain tensor powers of the Virasoro vertex operator algebra $L(\frac{1}{2},0)$, and we construct integral forms in certain modules for these algebras. When a triple of modules for a tensor power of $L(\frac{1}{2},0)$ have integral forms, we classify which intertwining operators among these modules respect the integral forms. As an application, we explore how these results might be used to obtain integral forms in framed vertex operator algebras.