The universal Racah-Wigner symbol for Uq(osp(1|2))

Abstract

We propose a new and elegant formula for the Racah-Wigner symbol of self-dual continuous series of representations of Uq(osp(1|2)). It describes the entire fusing matrix for both NS and R sector of N=1 supersymmetric Liouville field theory. In the NS sector, our formula is related to an expression derived in [1]. Through analytic continuation in the spin variables, our universal expression reproduces known formulas for the Racah-Wigner coefficients of finite dimensional representations.

27 pages, v2: discussion of analytic continuation of the main formula extended; some clarifications added

References in corpus (11)

• Instanton moduli spaces and bases in coset conformal field theory
• Coset conformal blocks and N=2 gauge theories
• On the fusion matrix of the N=1 Neveu-Schwarz blocks
• Chern-Simons Theory and S-duality
• Braiding and fusion properties of the Neveu-Schwarz super-conformal blocks
• On the relation between the modular double of U_q(sl(2,R)) and the quantum Teichmueller theory
• Braiding properties of the N=1 super-conformal blocks (Ramond sector)
• Liouville's Imaginary Shadow
• Analytic continuation formulae for the BPZ conformal block
• Super-Liouville - Double Liouville correspondence
• 6j symbols for the modular double, quantum hyperbolic geometry, and supersymmetric gauge theories

Cited by in corpus (18)

• Solving the Schwarzian via the Conformal Bootstrap
• Crossing Symmetry in Alpha Space
• Closure of the Operator Product Expansion in the Non-Unitary Bootstrap
• Solving 3d Gravity with Virasoro TQFT
• From Quantum Groups to Liouville and Dilaton Quantum Gravity
• The unitary subsector of generalized minimal models
• Degenerate operators in JT and Liouville (super)gravity
• Multiplicity-free $U_q(s{l}_N)$ 6-j symbols: relations, asymptotics, symmetries
• From Principal Series to Finite-Dimensional Solutions of the Yang-Baxter Equation
• A parafermionic hypergeometric function and supersymmetric 6j-symbols
• Comments on fusion matrix in N=1 super Liouville field theory
• Lens partition function, pentagon identity and star-triangle relation
• Wormholes with Ends of the World
• Quantum Groups as Global Symmetries
• Quantum group origins of edge states in double-scaled SYK
• On the 6j-symbols for SL(2,C) group
• Confluent Conformal Blocks of the Second Kind
• Heisenberg double and Drinfeld double of the quantum superplane