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Surface operators in 3d Topological Field Theory and 2d Rational Conformal Field Theory

Kapustin, Anton and Saulina, Natalia (2011) Surface operators in 3d Topological Field Theory and 2d Rational Conformal Field Theory. In: Mathematical Foundations of Quantum Field Theory and Perturbative String Theory. Proceedings of Symposia in Pure Mathematics. No.83. American Mathematical Society , Providence, RI, pp. 175-198. ISBN 978-0-8218-5195-1. http://resolver.caltech.edu/CaltechAUTHORS:20120302-140549797

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Abstract

We study surface operators in 3d Topological Field Theory and their relations with 2d Rational Conformal Field Theory. We show that a surface operator gives rise to a consistent gluing of chiral and anti-chiral sectors in the 2d RCFT. The algebraic properties of the resulting 2d RCFT, such as the classification of symmetry-preserving boundary conditions, are expressed in terms of properties of the surface operator. We show that to every surface operator one may attach a Morita-equivalence class of symmetric Frobenius algebras in the ribbon category of bulk line operators. This provides a simple interpretation of the results of Fuchs, Runkel and Schweigert on the construction of 2d RCFTs from Frobenius algebras. We also show that every topological boundary condition in a 3d TFT gives rise to a commutative Frobenius algebra in the category of bulk line operators. We illustrate these general considerations by studying in detail surface operators in abelian Chern-Simons theory.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
https://bookstore.ams.org/pspum-83PublisherBook Publisher
http://arxiv.org/abs/1012.0911arXivDiscussion Paper
ORCID:
AuthorORCID
Kapustin, Anton0000-0003-3903-5158
Alternate Title:Surface operators in 3d TFT and 2d rational CFT
Additional Information:© 2011 American Mathematical Society.
Group:Caltech Theory
Subject Keywords:High Energy Physics - Theory (hep-th); Quantum Algebra (math.QA)
Record Number:CaltechAUTHORS:20120302-140549797
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20120302-140549797
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:29571
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:14 May 2012 23:00
Last Modified:08 Aug 2018 17:22

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