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

• Published in: Letters in mathematical physics Vol. 104; no. 5; pp. 527 - 551
• Main Authors: Teschner, Jörg, Vartanov, Grigory
• Format: Journal Article
• Language: English
• 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
• ISSN: 0377-9017; 1573-0530
• DOI: 10.1007/s11005-014-0684-3

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...