Modular invariance of (logarithmic) intertwining operators
type: Item
instance of: scholarly article
title: Modular invariance of (logarithmic) intertwining operators
author: Yi-Zhi Huang
published in: Communications in Mathematical Physics
publication date: 2024-06-05T00:00:00Z
review text: Previously, Y. Zhu, in his 1990 PhD thesis (published as [\textit{Y. Zhu}, J. Am. Math. Soc. 9, No. 1, 237--302 (1996; Zbl 0854.17034)]), established a seminal result on the modular invariance of characters for rational \(C_2\)-cofinite vertex algebras, where characters are represented as modified graded traces. In 2004, \textit{M. Miyamoto} [Duke Math. J. 122, No. 1, 51--91 (2004; Zbl 1165.17311)] extended this result to \(C_2\)-cofinite vertex algebras without the rationality requirement, replacing graded traces with more general symmetric functions known as pseudotraces. Around the same time, the author [Commun. Contemp. Math. 7, No. 5, 649--706 (2005; Zbl 1124.11022)] generalized Zhu's result to products of intertwining operators within the rational framework. This current paper offers a unifying approach that broadens Miyamoto's and author's results, providing the most comprehensive modular invariance for products of intertwining operators. More precisely, Huang demonstrates that the spaces generated by analytic extensions of pseudo-\(q\)-traces (where \(q = e^{2 \pi i \tau}\)) shifted by \(-\frac{c}{24}\), of products of geometrically-modified (logarithmic) intertwining operators among grading-restricted generalized V-modules, remain invariant under modular transformations.
reviewed by: A. Milas
Mathematics Subject Classification ID: 17B69
Mathematics Subject Classification ID: 11F22
Mathematics Subject Classification ID: 81T40
zbMATH DE Number: 7860607
zbMATH Keywords: vertex operator algebras, modular invariance, intertwning operators
MaRDI profile type: Publication
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DOI: 10.1007/S00220-024-04983-Y
description: scientific article; zbMATH DE number 7860607