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000169956 1001_ $$0P:(DE-H253)PIP1005175$$aTeschner, Jörg$$b0$$eCorresponding Author
000169956 245__ $$a6j Symbols for the Modular Double, Quantum Hyperbolic Geometry, and Supersymmetric Gauge Theories
000169956 260__ $$aDordrecht [u.a.]$$bSpringer Science + Business Media B.V$$c2014
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000169956 520__ $$aWe revisit the definition of the 6j-symbols from the modular double of U_q(sl(2,R)), referred to as b-6j symbols. Our new results are (i) the identification of particularly natural normalization conditions, and (ii) new integral representations for this object. This is used to briefly discuss possible applications to quantum hyperbolic geometry, and to the study of certain supersymmetric gauge theories. We show, in particular, that the b-6j symbol has leading semiclassical asymptotics given by the volume of a non-ideal tetrahedron. We furthermore observe a close relation with the problem to quantize natural Darboux coordinates for moduli spaces of flat connections on Riemann surfaces related to the Fenchel-Nielsen coordinates. Our new integral representations finally indicate a possible interpretation of the b-6j symbols as partition functions of three-dimensional N=2 supersymmetric gauge theories.
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000169956 650_7 $$2INSPIRE$$agauge field theory: supersymmetry
000169956 650_7 $$2INSPIRE$$asupersymmetry: 2
000169956 650_7 $$2INSPIRE$$adimension: 3
000169956 650_7 $$2INSPIRE$$ageometry
000169956 650_7 $$2INSPIRE$$amodular
000169956 650_7 $$2INSPIRE$$apartition function
000169956 650_7 $$2INSPIRE$$aRiemann surface
000169956 650_7 $$2INSPIRE$$asemiclassical
000169956 650_7 $$2INSPIRE$$aquantization
000169956 650_7 $$2INSPIRE$$amoduli space
000169956 650_7 $$2INSPIRE$$afield theory: Liouville
000169956 650_7 $$2INSPIRE$$aapproximation: classical
000169956 650_7 $$2INSPIRE$$an-point function: 4
000169956 650_7 $$2INSPIRE$$aSU(2)
000169956 650_7 $$2INSPIRE$$aYang-Mills
000169956 650_7 $$2INSPIRE$$aChern-Simons term
000169956 650_7 $$2INSPIRE$$aClebsch-Gordan coefficients
000169956 65020 $$2Author$$aSUSY gauge theories 
000169956 65020 $$2Author$$ahyperbolic volumes 
000169956 65020 $$2Author$$amodular double 
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000169956 7001_ $$0P:(DE-H253)PIP1015705$$aVartanov, Grigory$$b1
000169956 773__ $$0PERI:(DE-600)1479697-1$$a10.1007/s11005-014-0684-3$$gVol. 104, no. 5, p. 527 - 551$$n5$$p527 - 551$$tLetters in mathematical physics$$v104$$x1573-0530$$y2014
000169956 7870_ $$0PHPPUBDB-21301$$aTeschner, J. et.al.$$d2012$$iIsParent$$rDESY-12-035 ; arXiv:1202.4698$$t6j symbols for the modular double, quantum hyperbolic geometry, and supersymmetric gauge theories
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