TheAdS5×S5superstring worldsheetSmatrix and crossing symmetry

2006/03/31 by Romuald A. Janik · 20 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic number #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Combinatorics #Geometry #Mathematical analysis #Mathematical physics #Mathematics #Matrix (chemical analysis) #Physics #Scalar (mathematics) #Superstring theory #Supersymmetry #hep-th #math-ph #math.MP #math.QA

paper · pdf · doi:10.1103/physrevd.73.086006

published as Phys.Rev.D73:086006,2006 · 27 pages, no figures; v2: sign typo fixed in (24), everything else unchanged

openalex publication_date 2006/04/18 · arxiv created 2007/01/11 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

An S matrix satisfying the Yang-Baxter equation with symmetries relevant to the AdS₅\ifmmode×\else\texttimes\fiS⁵ 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 AdS₅\ifmmode×\else\texttimes\fiS⁵ 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.

Citations

• Long-Range PSU(2,2|4) Bethe Ansaetze for Gauge Theory and Strings
• A Novel Long Range Spin Chain and PlanarN=4 Super Yang-Mills
• Integrable Hamiltonian for Classical Strings on AdS5 × S5
• The Dilatation Operator of Conformal N=4 Super Yang-Mills Theory
• The Large-N Limit of Superconformal Field Theories and Supergravity

Cited by

• Minimal solution of the AdS/CFT crossing equation
• Integrable twists in AdS/CFT
• Hopf algebra structure of the AdS/CFTS-matrix
• Constrained WZWN models on G/S⊗U(1)n and exchange algebra of G-primaries
• Reflecting magnon bound states
• Y-system, TBA and Quasi-Classical Strings in AdS 4 × CP3
• q-Poincaré invariance of the AdS3/CFT2 R-matrix
• On the spectrum of AdS3×S3×T4strings with Ramond–Ramond flux
• Note on the near flat limit for strings in the Maldacena-Nunez background
• Structure of the stringR-matrix
• Secret symmetries of type IIB superstring theory on \rm Ad\rm S₃ × S³ × M⁴
• The all-loop integrable spin-chain for strings on AdS3 × S 3 × T 4: the massive sector
• S-matrix algebra of theAdS2×S2superstring
• The dressing factor and crossing equations
• Five-loop anomalous dimension of twist-two operators
• Superstrings on AdS4× ℂℙ3as a coset sigma-model
• Extended Y-system for the AdS5/CFT4 correspondence
• On S-matrix factorization of the Landau-Lifshitz model
• Fusion for the one-dimensional Hubbard model
• Finite size giant magnon