Quantum Teichmüller theory and TQFT

Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearchpeer-review

Abstract

By using quantum Teichmüller theory, a new type of three-dimensional TQFT has been constructed with the following distinguishing features: it uses the combinatorial framework of shaped triangulations; it takes its values in the space of tempered distributions; the fundamental building block of the theory is given by Faddeev’s quantum dilogarithm. The semi-classical behavior and the geometrical ingredients suggest that the constructed TQFT is related to exact solution of quantum Chern-Simons theory with gauge group SL(2;C). We also remark that quantum Teichmüller theory itself admits an additional real parameter which preserves unitarity but affects the projective factor in the corresponding mapping class group representation.

Original languageEnglish
Title of host publicationXVIIth International Congress on Mathematical Physics
EditorsArne Jensen
Number of pages9
PublisherWorld Scientific
Publication date2013
Pages684-692
ChapterPart B
ISBN (Print)978-981-4449-23-6
ISBN (Electronic)978-981-4449-25-0
DOIs
Publication statusPublished - 2013
Externally publishedYes
EventXVIITH INTERNATIONAL CONGRESS ON MATHEMATICAL PHYSICS - Aalborg, Denmark
Duration: 6. Aug 201211. Aug 2012

Conference

ConferenceXVIITH INTERNATIONAL CONGRESS ON MATHEMATICAL PHYSICS
Country/TerritoryDenmark
CityAalborg
Period06/08/201211/08/2012

Keywords

  • Quantum theory
  • TQFT
  • Teichmüller space

Fingerprint

Dive into the research topics of 'Quantum Teichmüller theory and TQFT'. Together they form a unique fingerprint.

Cite this