The Hirota equation for string theory in AdS5xS5 from the fusion of line operators

Abstract

We present a perturbative derivation of the T-system that is believed to encode the exact spectrum of planar N=4 SYM. The T-system is understood as an operator identity between some special line operators, the quantum transfer matrices. By computing the quantum corrections in the process of fusion of transfer matrices, we show that the T-system holds up to first order in a semi-classical expansion. This derivation does not rely on any assumption. We also discuss the extension of the proof to other theories, including models describing string theory on various AdS spaces.

6 pages, 1 figure, Contribution to the proceedings of the "XVII European Workshop on String Theory 2011", Padova, Italy, 5-9 September 2011

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• On the quantization of continuous non-ultralocal integrable systems
• On the equivalence theorem for integrable systems
• Integrable theories and generalized graded Maillet algebras
• The r-matrix of the Alday-Arutyunov-Frolov model
• Worldsheet dilatation operator for the $AdS$ superstring