Generalized unitarity and the worldsheet S matrix in AdS_n x S^n x M^(10-2n)

Abstract

The integrability-based solution of string theories related to AdS(n)/CFT(n-1) dualities relies on the worldsheet S matrix. Using generalized unitarity we construct the terms with logarithmic dependence on external momenta at one- and two-loop order in the worldsheet S matrix for strings in a general integrable worldsheet theory. We also discuss aspects of calculations at higher orders. The S-matrix elements are expressed as sums of integrals with coefficients given in terms of tree-level worldsheet four-point scattering amplitudes. One-loop rational functions, not determined by two-dimensional unitarity cuts, are fixed by symmetry considerations. They play an important role in the determination of the two-loop logarithmic contributions. We illustrate the general analysis by computing the logarithmic terms in the one- and two-loop four-particle S-matrix elements in the massive worldsheet sectors of string theory in AdS_5 x S^5, AdS_4 x CP^3, AdS_3 x S^3 x S^3 x S^1 and AdS_3 x S^3 x T^4. We explore the structure of the S matrices and provide explicit evidence for the absence of higher-order logarithms and for the exponentiation of the one-loop dressing phase.

57 pages, Latex, 6 figures v2: minor misprints and misprints in equations in secs 7.1 and 7.2 corrected

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Cited by in corpus (24)

• The complete AdS_3 x S^3 x T^4 worldsheet S-matrix
• Dressing phases of AdS3/CFT2
• Massive S-matrix of AdS_3 x S^3 x T^4 superstring theory with mixed 3-form flux
• $Ad{S}_3\times S^3\times M^4$ string S-matrices from unitarity cuts
• Finite-gap equations for strings on AdS_3 x S^3 x T^4 with mixed 3-form flux
• Two-dimensional S-matrices from unitarity cuts
• The one-loop worldsheet S-matrix for the AdS(n) x S(n) x T(10-2n) superstring
• Precision calculation of 1/4-BPS Wilson loops in AdS${}_5\times S^5$
• $Ad{S}_3/CF{T}_2$, finite-gap equations and massless modes
• Integrable S-matrices, massive and massless modes and the AdS_2 x S^2 superstring
• One- and two-loop checks for the AdS(3) x S(3) x T(4) superstring with mixed flux
• The Effectiveness of Relativistic Invariance in AdS${}_3$
• The AdS(n) x S(n) x T(10-2n) BMN string at two loops
• The ${\mathrm{AdS}}_3\times {\mathrm{S}}^3\times {\mathrm{S}}^3\times {\mathrm{S}}^1$ worldsheet S matrix
• Integrable open spin-chains in AdS3/CFT2 correspondences
• The S-matrix algebra of the AdS2 X S2 superstring
• Non-planarity through unitarity in ABJM
• Worldsheet scattering for the GKP string
• One-loop spectroscopy of semiclassically quantized strings: bosonic sector
• A study of integrable form factors in massless relativistic AdS_3
• Norms and scalar products for AdS_3
• Remarks on the geometrical properties of semiclassically quantized strings
• Unitarity methods for scattering in two dimensions
• On regularizing the AdS superstring worldsheet