Journal Article

DESY-2014-02955

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png 6j Symbols for the Modular Double, Quantum Hyperbolic Geometry, and Supersymmetric Gauge Theories

Teschner, J. (Corresponding Author)DESY* ; Vartanov, G.DESY*

2014
Springer Science + Business Media B.V Dordrecht [u.a.]

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Please use a persistent id in citations: doi:10.1007/s11005-014-0684-3  doi:10.3204/DESY-2014-02955

Report No.: DESY-12-035; arXiv:1202.4698

Abstract: We revisit the definition of the 6j-symbols from the modular double of U_q(sl(2,R)), referred to as b-6j symbols. Our new results are (i) the identification of particularly natural normalization conditions, and (ii) 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-6j symbol has leading semiclassical asymptotics given by the volume of a non-ideal tetrahedron. We furthermore observe a close relation with the problem to quantize natural Darboux coordinates for moduli spaces of flat connections on Riemann surfaces related to the Fenchel-Nielsen coordinates. Our new integral representations finally indicate a possible interpretation of the b-6j symbols as partition functions of three-dimensional N=2 supersymmetric gauge theories.

Keyword(s): SUSY gauge theories (LCSH) ; hyperbolic volumes (LCSH) ; modular double (LCSH) ; gauge field theory: supersymmetry ; supersymmetry: 2 ; dimension: 3 ; geometry ; modular ; partition function ; Riemann surface ; semiclassical ; quantization ; moduli space ; field theory: Liouville ; approximation: classical ; n-point function: 4 ; SU(2) ; Yang-Mills ; Chern-Simons term ; Clebsch-Gordan coefficients

Note: © Springer Science+Business Media Dordrecht

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Contributing Institute(s):

1. Theorie-Gruppe (T)

Research Program(s):

1. 51x - Programm Elementarteilchenphysik - Topic unbekannt (POF2-51x) (POF2-51x)

Experiment(s):

1. No specific instrument

Appears in the scientific report 2014

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Database coverage:
; JCR ; Nationallizenz ; SCOPUS ; Science Citation Index ; Science Citation Index Expanded ; Thomson Reuters Master Journal List ; Web of Science Core Collection ; Zoological Record

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Linked articles:

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Preprint/Internal Report Teschner, J. ; Vartanov, G. S. ; DESY
6j symbols for the modular double, quantum hyperbolic geometry, and supersymmetric gauge theories
Red Report (2012)2012     Files  Fulltext by arXiv.org BibTeX | EndNote: XML, Text | RIS

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