Integrability for the Full Spectrum of Planar AdS/CFT II

Details Integrability for the Full Spectrum of Planar AdS/CFT II Integrability for the Full Spectrum of Planar AdS/CFT II

2009-02-25

arxiv.org/abs/0902.4458v4

Physics

High Energy Physics

High Energy Physics - Theory

Journal version

Scientific paper

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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