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arXiv · 1804.06741

Quantum spectral curve for the $η$-deformed AdS$_5 \times $S$^5$ superstring

Rob Klabbers
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Abstract

In this thesis we discuss how one can derive the quantum spectral curve for the $η$-deformed AdS$_5 \times S^5$ superstring, an integrable deformation of the AdS$_5 \times $S$^5$ superstring with quantum group symmetry. This model can be viewed as a trigonometric version of the AdS$_5 \times $S$^5$ superstring, like the Heisenberg xxz spin chain is a trigonometric version of the xxx spin chain. Our derivation starts from the ground-state thermodynamic Bethe ansatz equations and discusses the construction of both the undeformed and the $η$-deformed quantum spectral curve. We reformulate it first as an analytic $Y$-system, and map this to an analytic $T$-system which upon suitable gauge fixing leads to a $\mathbf{P}μ$ 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 $η$-deformed string and its quantum spectral curve interpolate between the AdS$_5 \times $S$^5$ superstring and a superstring on "mirror" AdS$_5 \times $S$^5$, reflecting a more general relationship between the spectral and thermodynamic data of the $η$-deformed string. The thesis is set up such that it simultaneously reviews the development of the undeformed AdS$_5 \times $S$^5$ quantum spectral curve.

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Rob Klabbers. 2018-11-20. Quantum spectral curve for the $η$-deformed AdS$_5 \times $S$^5$ superstring. https://arxiv.org/abs/1804.06741

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