Logarithmic conformal field theory, log-modular tensor categories and modular forms

T Creutzig, T Gannon - … Physics A: Mathematical and Theoretical, 2017 - iopscience.iop.org
… of Argyres-Douglas theories [C2]. As we will mention later in conjecture 3.3, the semi-simplification
of a log-modular tensor category is expected to be a modular tensor category. This …

Twisted Modules and G-equivariantization in Logarithmic Conformal Field Theory

R McRae - Communications in Mathematical Physics, 2021 - Springer
modules for the chiral algebra) because of the logarithmic tensor category theory of Huang,
… -semisimple or rigid braided tensor categories \({\mathcal {C}}\) of modules for the fixed-point …

On the applicability of logarithmic tensor category theory

YZ Huang - arXiv preprint arXiv:1702.00133, 2017 - arxiv.org
… structure (including a ribbon structure) on a module category C for a suitable vertex operator
algebra or more general vertex algebra V . In this paper we broaden the applicability of this …

Affine Lie algebras and tensor categories

YZ Huang - arXiv preprint arXiv:1811.05123, 2018 - arxiv.org
… of various tensor category structures on module categories for … proved using the logarithmic
tensor category theory of Lepowsky, … The logarithmic tensor category theory reduces the …

Braided tensor categories of admissible modules for affine Lie algebras

T Creutzig, YZ Huang, J Yang - Communications in Mathematical Physics, 2018 - Springer
… structure (with a twist) by using the logarithmic tensor category theory developed in [HLZ1,HLZ2,HLZ3,HLZ4,HLZ5,HLZ6,HLZ7,HLZ8,HLZ9]
and [H7]. The work carried out in the present …

Ribbon tensor structure on the full representation categories of the singlet vertex algebras

T Creutzig, R McRae, J Yang - Advances in Mathematics, 2023 - Elsevier
… ( p ) -modules, and we prove that both tensor categories O M ( … extension theory to show that
the representation categories … Even the construction of logarithmic modules is a difficult task: …

Tensor categories of affine Lie algebras beyond admissible levels

T Creutzig, J Yang - Mathematische Annalen, 2021 - Springer
… We aim to discuss braided tensor categories of finite length generalized modules for a general
affine … axiom in order to check the applicability of the logarithmic tensor category theory. …

[图书][B] Dualizable tensor categories

C Douglas, C Schommer-Pries, N Snyder - 2020 - ams.org
… Schweigert’s work on logarithmic conformal field theory [FS10]. … separable modules and
separable tensor categories: … A finite module category CM over a semisimple tensor category is …

Characterizing braided tensor categories associated to logarithmic vertex operator algebras

T Creutzig, S Lentner, M Rupert - arXiv preprint arXiv:2104.13262, 2021 - arxiv.org
tensor category CV of V modules, then the category of W-modules that lie in CV is a vertex
tensor category … It is believed but unproven that the category of ordinary modules of the singlet …

Tensor categories for vertex operator superalgebra extensions

T Creutzig, S Kanade, R McRae - arXiv preprint arXiv:1705.05017, 2017 - arxiv.org
… If the vertex tensor category of either V -modules or C-modules is understood, then our
results … , vertex tensor categories for vertex operator algebras in logarithmic conformal field …