On a categorical structure of the set of all CFTs

TL;DR

This paper reveals a categorical framework for all conformal field theories (CFTs), showing they form a monoidal strict 2-category with morphisms representing deformations and symmetries.

Contribution

It introduces a novel categorical structure for CFTs, providing a mathematical foundation for their relationships and symmetries.

Findings

Set of all CFTs forms a monoidal strict 2-category

1-morphisms are sequences of deformations

2-morphisms are determined by 0-form symmetries

Abstract

We identify a categorical structure of the set of all CFTs. In particular, we show that the set of all CFTs has a natural monoidal strict $2$-category structure with the $1$-morphisms being sequences of deformations and $2$-morphisms determined by $0$-form symmetries of the CFTs.