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\({\mathrm{AdS}}_{3}/{\mathrm{CFT}}_{2}\) and \(q\)-Poincaré superalgebras. (English) Zbl 1352.81039

Summary: We discover that a certain deformation of the 1+1 dimensional Poincaré superalgebra is exactly realised in the massless sector of the \({\mathrm{AdS}}_{3}/{\mathrm{CFT}}_{2}\) integrable scattering problem. Deformed Poincaré superalgebras were previously noticed to appear in the \({\mathrm{AdS}}_{5}/{\mathrm{CFT}}_{4}\) correspondence – which displays only massive excitations, but they were there only a partial symmetry. We obtain a representation of the boost operator and its coproduct, and show that the comultiplication exactly satisfies the homomorphism property. We present a classical limit, and finally speculate on an analogy with the physics of phonons.

MSC:

81R50 Quantum groups and related algebraic methods applied to problems in quantum theory
81T20 Quantum field theory on curved space or space-time backgrounds
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
17B37 Quantum groups (quantized enveloping algebras) and related deformations
17A70 Superalgebras
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