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

TY - JOUR

T1 - Review of AdS/CFT Integrability, Chapter II.4: The Spectral Curve

AU - Schafer-Nameki, Sakura

PY - 2012/1

Y1 - 2012/1

N2 - 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.

AB - 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.

U2 - 10.1007/s11005-011-0525-6

DO - 10.1007/s11005-011-0525-6

M3 - Literature review

SN - 0377-9017

VL - 99

SP - 169

EP - 190

JO - LETTERS IN MATHEMATICAL PHYSICS

JF - LETTERS IN MATHEMATICAL PHYSICS

IS - 1-3

ER -