Geometric construction of modular functors from Conformal Field Theory

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

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''.

Construction of the Witten-Reshetikhin-Turaev TQFT from conformal field theory

In [AU2] we constructed the vacua modular functor based on the sheaf of vacua theory developed in [TUY] and the abelian analog in [AU1]. We here provide an explicit isomorphism from the modular functor underlying the skein-theoretic model for the Witten-Reshetikhin-Turaev TQFT due to Blanchet, Habbeger, Masbaum and Vogel to the vacua modular functor. This thus provides a geometric construction of the TQFT constructed first by Witten-Reshetikhin-Turaev from the quantum group associated to SL(N).

Modular Curvature for Noncommutative Two-Tori

In this paper we investigate the curvature of conformal deformations by noncommutative Weyl factors of a flat metric on a noncommutative 2-torus, by analyzing in the framework of spectral triples functionals associated to perturbed Dolbeault operators. The analogue of Gaussian curvature turns out to be a sum of two functions in the modular operator corresponding to the non-tracial weight defined by the conformal factor, applied to expressions involving derivatives of the same factor. The first is a generating function for the Bernoulli numbers and is applied to the noncommutative Laplacian of …

Virasoro 共形块与来自Liouville CFT的模函子

Virasoro Conformal Blocks and modular functor from Liouville CFT

本文从Liouville CFT构造了亏格g、m个标记点黎曼曲面上Virasoro共形块的全局全纯截面，满足Ward恒等式，并证明其承载映射类群的射影酉表示，对Moore-Seiberg移动有酉同构。

一致方法用于共形和模不变量

A unified approach to conformal and modular invariants

本文提出一种统一方法，通过边界参数化 bordered Riemann 面或紧致面的共形映射，构造共形不变量，并展示其作为 generalized 模不变量和 Segal-Vafa 级数空间上的函数，同时探讨其在共形不变量中的应用。