Quantum Spectral Curve for the eta-deformed AdS_5xS^5 superstring

Abstract

The spectral problem for the ${\mathrm{AdS}}_5\times {\mathrm{S}}^5$ superstring and its dual planar maximally supersymmetric Yang-Mills theory can be efficiently solved through a set of functional equations known as the quantum spectral curve. We discuss how the same concepts apply to the $\eta$-deformed ${\mathrm{AdS}}_5\times {\mathrm{S}}^5$ superstring, an integrable deformation of the ${\mathrm{AdS}}_5\times {\mathrm{S}}^5$ superstring with quantum group symmetry. This model can be viewed as a trigonometric version of the ${\mathrm{AdS}}_5\times {\mathrm{S}}^5$ superstring, like the relation between the XXZ and XXX spin chains, or the sausage and the ${\mathrm{S}}^2$ sigma models for instance. We derive the quantum spectral curve for the $\eta$-deformed string by reformulating the corresponding ground-state thermodynamic Bethe ansatz equations as an analytic $Y$ system, and map this to an analytic $T$ system which upon suitable gauge fixing leads to a $\mathbf{P}\mu$ system -- the quantum spectral curve. We then discuss constraints on the asymptotics of this system to single out particular excited states. At the spectral level the $\eta$-deformed string and its quantum spectral curve interpolate between the ${\mathrm{AdS}}_5\times {\mathrm{S}}^5$ superstring and a superstring on "mirror" ${\mathrm{AdS}}_5\times {\mathrm{S}}^5$, reflecting a more general relationship between the spectral and thermodynamic data of the $\eta$-deformed string. In particular, the spectral problem of the mirror ${\mathrm{AdS}}_5\times {\mathrm{S}}^5$ string, and the thermodynamics of the undeformed ${\mathrm{AdS}}_5\times {\mathrm{S}}^5$ string, are described by a second rational limit of our trigonometric quantum spectral curve, distinct from the regular undeformed limit.

32+37 pages; 6 figures. v2: added references

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Cited by in corpus (22)

• Quantum Spectral Curve and Structure Constants in N=4 SYM: Cusps in the Ladder Limit
• Supergravity backgrounds of the eta-deformed AdS2 x S2 x T6 and AdS5 x S5 superstrings
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• Yang-Baxter Deformations Beyond Coset Spaces (a slick way to do TsT)
• Introduction to the Spectrum of N=4 SYM and the Quantum Spectral Curve
• Unimodular jordanian deformations of integrable superstrings
• The Hagedorn temperature of AdS5/CFT4 at finite coupling via the Quantum Spectral Curve
• Exploring the spectrum of planar $Ad{S}_4/CF{T}_3$ at finite coupling
• A review of the AdS/CFT Quantum Spectral Curve
• Quantum Spectral Curve of $\gamma$-twisted $\mathcal{N}=4$ SYM theory and fishnet CFT
• Solving the Hagedorn temperature of AdS5/CFT4 via the Quantum Spectral Curve: Chemical potentials and deformations
• Homogeneous Yang-Baxter deformations as undeformed yet twisted models
• On Yang-Baxter models, twist operators, and boundary conditions
• Quantum Anisotropic Sigma and Lambda Models as Spin Chains
• Semiclassical spectrum of a Jordanian deformation of $Ad{S}_5\times S^5$
• The Tensionless Limit of Pure-Ramond-Ramond AdS3/CFT2
• Probing analytical and numerical integrability: The curious case of $(Ad{S}_5\times S^5{)}_{\eta }$
• On analytical perturbative solution of ABJM quantum spectral curve
• ABJM quantum spectral curve at twist 1: algorithmic perturbative solution
• Bethe Ansatz for Quantum-Deformed Strings
• Classical Spectral Curve of the AdS_5 x S^5 Lambda Superstring
• On exactly solvable Yang-Baxter models and enhanced symmetries