On quantum deformations of $Ad{S}_3\times S^3\times T^4$ and mirror duality

Abstract

We consider various integrable two-parameter deformations of the $Ad{S}_3\times S^3\times T^4$ superstring with quantum group symmetry. Working on the string worldsheet in light-cone gauge and to quadratic order in fermions, we obtain their common massive tree-level two-body S matrix, which matches the expansion of the conjectured exact $q$-deformed S matrix. We then analyze the behavior of the exact S matrix under mirror transformation -- a double Wick rotation on the worldsheet -- and find that it satisfies a mirror duality relation analogous to the distinguished $q$-deformed $Ad{S}_5\times S^5$ S matrix in the one parameter deformation limit. Finally, we show that the fermionic $q$-deformed $Ad{S}_5\times S^5$ S matrix also satisfies such a relation.

30+6 pages

References in corpus (15)

• 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
• Towards a two-parameter q-deformation of AdS_3 x S^3 x M^4 superstrings
• On the exact spectrum and mirror duality of the (AdS_5 x S^5)_eta superstring
• Kappa-symmetry of superstring sigma model and generalized 10d supergravity equations
• 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
• On the Dressing Factors, Bethe Equations and Yangian Symmetry of Strings on AdS3 x S3 x T4
• Generalized Supergravity Equations and Generalized Fradkin-Tseytlin Counterterm
• Relaxing unimodularity for Yang-Baxter deformed strings
• S matrix for a three-parameter integrable deformation of $Ad{S}_3\times S^3$ strings
• Three-parameter deformation of $\mathbb{R}\times S^3$ in the Landau-Lifshitz limit

Cited by in corpus (5)

• Integrable supersymmetric deformations of $\mathrm{Ad}{\mathrm{S}}_3\times {\mathrm{S}}^3\times {\mathrm{T}}^4$
• Integrable deformations of AdS/CFT
• Bethe Ansatz for Quantum-Deformed Strings
• Quantum deformation of cubic string field theory
• Pulsating string solution and stability in two parameter $\chi$-deformed background