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

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Abstract

We review the spectral curve for the classical string in AdS 5 × S 5. Classical integrability of the AdS 5 × 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 \({\mathbb{R} \times S^3\subset AdS_5 \times S^5}\) .

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Authors and Affiliations

  1. Kavli Institute for Theoretical Physics, University of California, Santa Barbara, 93106, CA, USA

    Sakura Schäfer-Nameki

  2. Department of Mathematics, King’s College, The Strand, London, WC2R 2LS, UK

    Sakura Schäfer-Nameki

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  1. Sakura Schäfer-Nameki
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Schäfer-Nameki, S. Review of AdS/CFT Integrability, Chapter II.4: The Spectral Curve. Lett Math Phys 99, 169–190 (2012). https://doi.org/10.1007/s11005-011-0525-6

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