Review of AdS/CFT Integrability, Chapter II.4: The Spectral Curve

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We review the spectral curve for the classical string in AdS(5) x S-5. Classical integrability of the AdS(5) x S-5 string implies the existence of a flat connection, whose monodromies generate an infinite set of conserved charges. The spectral curve is constructed out of the quasi-momenta, which are eigenvalues of the monodromy matrix, and each finite-gap classical solution can be characterized in terms of such a curve. This provides a concise and powerful description of the classical solution space. In addition, semi-classical quantization of the string can be performed in terms of the quasi-momenta. We review the general frame-work of the semi-classical quantization in this context and exemplify it with the circular string solution which is supported on R x S-3 subset of AdS(5) x S-5.

Original languageEnglish
Pages (from-to)169-190
Number of pages22
Issue number1-3
Publication statusPublished - Jan 2012


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