On the infinite dimensional hidden symmetries. II. $q_R$-conformal modular functor

TL;DR

This paper explores $q_R$-conformal modular functors as deformations and Berezin quantizations of classical conformal modular functors, extending the understanding of infinite-dimensional hidden symmetries in mathematical physics.

Contribution

It introduces and analyzes $q_R$-conformal modular functors as deformations of classical structures, providing new insights into their role as Berezin quantizations of conformal modular functors.

Findings

$q_R$-conformal modular functors are deformations of classical conformal modular functors.

These functors can be viewed as Berezin quantizations of the classical structures.

The work extends the framework of modular functors to infinite-dimensional hidden symmetries.

Abstract

The article is devoted to the $q_R$-conformal modular functors, which being ``deformations'' of the conformal modular functor (the projective representation of the category $Train(Diff_+(S^1))$, the train of the group $Diff_+(S^1)$ of all orientation preserving diffeomorphisms of a circle) in the class of all projective modular functors (the projective representations of the category $Train(PSL(2,R))$, the train of the projective group $PSL(2,R)$), may be regarded as its ``Berezin quantizations''.