Integrability for the Full Spectrum of Planar AdS/CFT II
Nikolay Gromov, Vladimir Kazakov, Andrii Kozak, Pedro Vieira
TL;DR
This paper derives a comprehensive set of integral equations for the spectrum of states in planar AdS/CFT using thermodynamic Bethe ansatz, confirming the Y-system and providing detailed equations for the sl(2) sector.
Contribution
It introduces an infinite set of integral non-linear equations for AdS/CFT spectrum and confirms the Y-system conjecture, including explicit equations for the sl(2) sector.
Findings
Derived integral equations for the spectrum in AdS/CFT
Confirmed the Y-system for all operators
Established properties of kernels and free terms
Abstract
Using the thermodynamical Bethe ansatz method we derive an infinite set of integral non-linear equations for the spectrum of states/operators in AdS/CFT. The Y-system conjectured in arXiv:0901.3753 for the spectrum of all operators in planar N=4 SYM theory follows from these equations. In particular, we present the integral equations for the spectrum of all operators within the sl(2) sector. We prove that all the kernels and free terms entering these TBA equations are real and have nice fusion properties in the relevant mirror kinematics. We find the analogue of DHM formula for the dressing kernel in the mirror kinematics.
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