Science-advisor
REGISTER info/FAQ
Login
username
password
     
forgot password?
register here
 
Research articles
  search articles
  reviews guidelines
  reviews
  articles index
My Pages
my alerts
  my messages
  my reviews
  my favorites
 
 
Stat
Members: 3643
Articles: 2'488'730
Articles rated: 2609

29 March 2024
 
  » » arxiv » 248196

 Article forum


Picard groups in rational conformal field theory
Jürg Fröhlich ; Jürgen Fuchs ; Ingo Runkel ; Christoph Schweigert ;
Date 23 Nov 2004
Subject Category Theory; Mathematical Physics; Quantum Algebra MSC-class: 81T40,18D10,18D35,81T45 | math.CT hep-th math-ph math.MP math.QA
AbstractAlgebra and representation theory in modular tensor categories can be combined with tools from topological field theory to obtain a deeper understanding of rational conformal field theories in two dimensions: It allows us to establish the existence of sets of consistent correlation functions, to demonstrate some of their properties in a model-independent manner, and to derive explicit expressions for OPE coefficients and coefficients of partition functions in terms of invariants of links in three-manifolds. We show that a Morita class of (symmetric special) Frobenius algebras $A$ in a modular tensor category $calc$ encodes all data needed to describe the correlators. A Morita-invariant formulation is provided by module categories over $calc$. Together with a bimodule-valued fiber functor, the system (tensor category + module category) can be described by a weak Hopf algebra. The Picard group of the category $calc$ can be used to construct examples of symmetric special Frobenius algebras. The Picard group of the category of $A$-bimodules describes the internal symmetries of the theory and allows one to identify generalized Kramers-Wannier dualities.
Source arXiv, math.CT/0411507
Services Forum | Review | PDF | Favorites   
 

No message found in this article forum.  You have a question or message about this article? Ask the community and write a message in the forum.
If you want to rate this article, please use the review section..

Subject of your forum message:
Write your forum message below (min 50, max 2000 characters)

2000 characters left.
Please, read carefully your message since you cannot modify it after submitting.

  To add a message in the forum, you need to login or register first. (free): registration page






ScienXe.org
» my Online CV
» Free


News, job offers and information for researchers and scientists:
home  |  contact  |  terms of use  |  sitemap
Copyright © 2005-2024 - Scimetrica