The AdS_5xS^5 superstring worldsheet S-matrix and crossing symmetry

Abstract

An S-matrix satisying the Yang-Baxter equation with symmetries relevant to the AdS_5xS^5 superstring has recently been determined up to an unknown scalar factor. Such scalar factors are typically fixed using crossing relations, however due to the lack of conventional relativistic invariance, in this case its determination remained an open problem. In this paper we propose an algebraic way to implement crossing relations for the AdS_5xS^5 superstring worldsheet S-matrix. We base our construction on a Hopf-algebraic formulation of crossing in terms of the antipode and introduce generalized rapidities living on the universal cover of the parameter space which is constructed through an auxillary, coupling constant dependent, elliptic curve. We determine the crossing transformation and write functional equations for the scalar factor of the S-matrix in the generalized rapidity plane.

arXiv comment27 pages, no figures; v2: sign typo fixed in (24), everything else unchanged

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• Quantum Scattering of Giant Magnons
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• Inelastic Magnon Scattering
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• On $Ad{S}_2/CF{T}_1$ transfer matrices, Bethe ansatz and scale invariance
• The high spin expansion of twist sector dimensions: the planar N=4 super Yang-Mills theory
• Free field representation of the ZF algebra of the SU(N)xSU(N) PCF model
• The Ising model and planar N=4 Yang-Mills
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• Integrable systems and AdS/CFT duality
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• On two-dimensional quasitopological field theories
• On the dressing phase in the SL(2) Bethe Ansatz
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• PSU(2,2|4) Exchange Algebra of N=4 Superconformal Multiplets
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• A note on the Near Flat Limit for strings in the Maldacena-Nunez background
• Matrix Reduction and the su(2|2) superalgebra in AdS/CFT
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• Exact Results in Supersymmetric Gauge Theories
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• Solving some gauge systems at infinite N
• Commuting Conformal and Dual Conformal Symmetries in the Regge limit
• Gauge-String Dualities and Some Applications
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• Unitarity methods for scattering in two dimensions
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