First-principles derivation of the AdS/CFT Y-systems

Details First-principles derivation of the AdS/CFT Y-systems First-principles derivation of the AdS/CFT Y-systems

2011-08-24

arxiv.org/abs/1108.4927v2

Physics

High Energy Physics

High Energy Physics - Theory

45 pages, 5 figures; v2: minor additions, JHEP version

Scientific paper

We provide a first-principles, perturbative derivation of the AdS5/CFT4 Y-system that has been proposed to solve the spectrum problem of N=4 SYM. The proof relies on the computation of quantum effects in the fusion of some loop operators, namely the transfer matrices. More precisely we show that the leading quantum corrections in the fusion of transfer matrices induce the correct shifts of the spectral parameter in the T-system. As intermediate steps we study UV divergences in line operators up to first order and compute the fusion of line operators up to second order for the pure spinor string in AdS5xS5. We also argue that the derivation can be easily extended to other integrable models, some of which describe string theory on AdS4, AdS3 and AdS2 spacetimes.

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