The twisted story of worldsheet scattering in $\eta$-deformed $Ad{S}_5\times S^5$

Abstract

We study the worldsheet scattering theory of the $\eta$ deformation of the AdS${}_5\times$S${}^5$ superstring corresponding to the purely fermionic Dynkin diagram. This theory is a Weyl-invariant integrable deformation of the AdS${}_5\times$S${}^5$ superstring, with trigonometric quantum-deformed symmetry. We compute the two-body worldsheet S matrix of this string in the light-cone gauge at tree level to quadratic order in fermions. The result factorizes into two elementary blocks, and solves the classical Yang-Baxter equation. We also determine the corresponding exact factorized S matrix, and show that its perturbative expansion matches our tree-level results, once we correctly identify the deformed light-cone symmetry algebra of the string. Finally, we briefly revisit the computation of the corresponding S matrix for the $\eta$ deformation based on the distinguished Dynkin diagram, finding a tree-level S matrix that factorizes and solves the classical Yang-Baxter equation, in contrast to previous results.

40 pages, published in JHEP, v4: minor clarifications

References in corpus (12)

• Derivation of the action and symmetries of the q-deformed AdS_5 x S^5 superstring
• Target space supergeometry of $\eta$ and $\lambda$-deformed strings
• Quantum Deformations of the One-Dimensional Hubbard Model
• Lunin-Maldacena backgrounds from the classical Yang-Baxter equation -- Towards the gravity/CYBE correspondence
• The ${\mathrm{AdS}}_5\times {\mathrm{S}}^5$ mirror model as a string
• Double Wick rotating Green-Schwarz strings
• An Integrability Primer for the Gauge-Gravity Correspondence: an Introduction
• Quantum correction to generalized T-dualities
• ${\alpha }^{\prime }$-corrected Poisson-Lie T-duality
• Unimodular jordanian deformations of integrable superstrings
• Integrable sigma models and 2-loop RG flow
• Generalized Supergravity Equations and Generalized Fradkin-Tseytlin Counterterm

Cited by in corpus (5)

• Yang-Baxter and the Boost: splitting the difference
• Integrable supersymmetric deformations of $\mathrm{Ad}{\mathrm{S}}_3\times {\mathrm{S}}^3\times {\mathrm{T}}^4$
• Integrable bootstrap for AdS3/CFT2 correlation functions
• On quantum deformations of $Ad{S}_3\times S^3\times T^4$ and mirror duality
• On exactly solvable Yang-Baxter models and enhanced symmetries