The AdS 5 ×S 5 superstring worldsheet S matrix and crossing symmetry

By Romuald A. Janik. 2006

453 citations recorded by the source corpus.

An S matrix satisfying the Yang-Baxter equation with symmetries relevant to the AdS{sub 5}xS{sup 5} superstring recently has 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{sub 5}xS{sup 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.

Subfields: Algebra and Number Theory, Geometry and Topology, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/c49ae45dc79cfcacc46a2dce44cc181ee1bf8cfc

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Citations in the corpus

Dressing and wrapping (2007, background): “The understanding of its necessity and structure was subsequently refined in a series of important papers [ 12 ].”
Quantum spectral curve for arbitrary state/operator in AdS5/CFT4 (2014, background): “23) an analytic continuation [42] of the crossing equation [43], hence we can immediately write the solution:”
Wrapping interactions at strong coupling: The giant magnon (2007, methodology): “ above equation deﬁnes a torus, so equivalently one may use a parametrization by a single complex parameter (generalized rapidity) in the complex plane being the universal covering space of the torus [14]. We will not, however, use this parametrization in the present paper. The energy and momentum a”
Five-loop anomalous dimension of twist-two operators (2009, background): “tic Bethe equations (ABE) was conjectured [14] up to the so caed dre ssing factor, which only contributes starting from the four-loop order. Subsequently, relying on the crossing equation proposed in [15] and assuming certain transcendentaty prop erties, it was possible to uniquely ﬁx this factor [1”
Dressing the Giant Magnon (2006, background): “It is an important open problem to determine an overall λ-dependent phase factor in the magnon S-matrix [32,33], whose zeros and poles must contain information about the spectrum of magnon bound states.”
Finite-size effects from giant magnons (2006, methodology): “Using the Hopf-algebraic formulation of crossing in terms of an antipode, a functional equation for the dressing factor was derived in [4].”
Integrability and the AdS3/CFT2 correspondence (2009, unknown): “The experience with AdS5/CFT4 [14] and AdS4/CFT3 [17, 18] systems shows that the quantum Bethe equations are very constrained by symmetries [14, 19] and can be almost uniquely reconstructed from their semiclassical counterparts [20].”
Four-loop perturbative Konishi from strings and finite size effects for multiparticle states (2008, background): “In fact it is at the level of determining this scalar factor that the symmetry between the spin chain and worldsheet QFT picture is broken as the requirement of crossing symmetry [18] is definitely of a worldsheet QFT origin.”