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arXiv · hep-th/0606287

A Symplectic Structure for String Theory on Integrable Backgrounds

Nick Dorey·Benoit Vicedo
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Abstract

We define regularised Poisson brackets for the monodromy matrix of classical string theory on R x S^3. The ambiguities associated with Non-Ultra Locality are resolved using the symmetrisation prescription of Maillet. The resulting brackets lead to an infinite tower of Poisson-commuting conserved charges as expected in an integrable system. The brackets are also used to obtain the correct symplectic structure on the moduli space of finite-gap solutions and to define the corresponding action-angle variables. The canonically-normalised action variables are the filling fractions associated with each cut in the finite-gap construction. Our results are relevant for the leading-order semiclassical quantisation of string theory on AdS_5 x S^5 and lead to integer-valued filling fractions in this context.

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Nick Dorey, Benoit Vicedo. 2007-02-19. A Symplectic Structure for String Theory on Integrable Backgrounds. https://doi.org/10.1088/1126-6708%2F2007%2F03%2F045

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