# On classification of extremal non-holomorphic conformal field theories

@article{Tener2016OnCO,
title={On classification of extremal non-holomorphic conformal field theories},
author={James E. Tener and Zhenghan Wang},
journal={arXiv: Mathematical Physics},
year={2016}
}
• Published 13 November 2016
• Mathematics
• arXiv: Mathematical Physics
Rational chiral conformal field theories are organized according to their genus, which consists of a modular tensor category $\mathcal{C}$ and a central charge $c$. A long-term goal is to classify unitary rational conformal field theories based on a classification of unitary modular tensor categories. We conjecture that for any unitary modular tensor category $\mathcal{C}$, there exists a unitary chiral conformal field theory $V$ so that its modular tensor category $\mathcal{C}_V$ is $\mathcal… 18 Citations In and around abelian anyon models • Mathematics • 2020 Anyon models are algebraic structures that model universal topological properties in topological phases of matter and can be regarded as mathematical characterization of topological order in two Galois symmetry induced by Hecke relations in rational conformal field theory and associated modular tensor categories • Mathematics • 2019 Hecke operators relate characters of rational conformal field theories (RCFTs) with different central charges, and extend the previously studied Galois symmetry of modular representations and fusion Double-Janus linear sigma models and generalized reciprocity for Gauss sums • Mathematics • 2019 We study the supersymmetric partition function of a 2d linear$\sigma$-model whose target space is a torus with a complex structure that varies along one worldsheet direction and a Kahler modulus Wronskian indices and rational conformal field theories • Mathematics • 2021 The classification scheme for rational conformal field theories, given by the Mathur-Mukhi-Sen (MMS) program, identifies a rational conformal field theory by two numbers: ( n, l ). n is the number of Conformal Field Theories as Scaling Limit of Anyonic Chains • Physics Communications in Mathematical Physics • 2018 We provide a mathematical definition of a low energy scaling limit of a sequence of general non-relativistic quantum theories in any dimension, and apply our formalism to anyonic chains. We formulate Establishing strongly-coupled 3D AdS quantum gravity with Ising dual using all-genus partition functions • Physics • 2019 We study 3D pure Einstein quantum gravity with negative cosmological constant, in the regime where the AdS radius$l$is of the order of the Planck scale. Specifically, when the Brown-Henneaux A mathematical theory of gapless edges of 2d topological orders. Part I • Physics, Mathematics Journal of High Energy Physics • 2020 This is the first part of a two-part work on a unified mathematical theory of gapped and gapless edges of 2d topological orders. We analyze all the possible observables on the 1+1D world sheet of a Classifying three-character RCFTs with Wronskian Index equalling$\mathbf{0}$or$\mathbf{2}\$.
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