6j Symbols for the Modular Double, Quantum Hyperbolic Geometry, and Supersymmetric Gauge Theories

We revisit the definition of the 6 j symbols from the modular double of U q ( sl ( 2 , R ) ) , referred to as b-6 j symbols. Our new results are (1) the identification of particularly natural normalization conditions, and (2) new integral representations for this object. This is used to briefly disc...

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Bibliographic Details
Published inLetters in mathematical physics Vol. 104; no. 5; pp. 527 - 551
Main Authors Teschner, Jörg, Vartanov, Grigory
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.05.2014
Subjects
Complex Systems
Geometry
Group Theory and Generalizations
Mathematical and Computational Physics
Physics
Physics and Astronomy
Theoretical
modular double
81R50
51M10
hyperbolic volumes
SUSY gauge theories
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Summary:We revisit the definition of the 6 j symbols from the modular double of U q ( sl ( 2 , R ) ) , referred to as b-6 j symbols. Our new results are (1) the identification of particularly natural normalization conditions, and (2) new integral representations for this object. This is used to briefly discuss possible applications to quantum hyperbolic geometry, and to the study of certain supersymmetric gauge theories. We show, in particular, that the b-6 j symbol has leading semiclassical asymptotics given by the volume of a non-ideal tetrahedron. Our new integral representations finally indicate a possible interpretation of the b-6 j symbols as partition functions of non-abelian three-dimensional N = 2 supersymmetric gauge theories.
ISSN:0377-9017
1573-0530
DOI:10.1007/s11005-014-0684-3