Semiclassical integrability in AdS/CFT

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Gauge Theory Correlators from Non-Critical String Theory

I. Klebanov, S. S. Gubser, A. M. POLYAKOV (1998)

We suggest a means of obtaining certain Green's functions in 3+1-dimensional \({\cal N} = 4\) supersymmetric Yang-Mills theory with a large number of colors via non-critical string theory. The non-critical string theory is related to critical string theory in anti-deSitter background. We introduce a boundary of the anti-deSitter space analogous to a cut-off on the Liouville coordinate of the two-dimensional string theory. Correlation functions of operators in the gauge theory are related to the dependence of the supergravity action on the boundary conditions. From the quadratic terms in supergravity we read off the anomalous dimensions. For operators that couple to massless string states it has been established through absorption calculations that the anomalous dimensions vanish, and we rederive this result. The operators that couple to massive string states at level \(n\) acquire anomalous dimensions that grow as \(2\left (n g_{YM} \sqrt {2 N} )^{1/2}\) for large `t Hooft coupling. This is a new prediction about the strong coupling behavior of large \(N\) SYM theory.

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Theory of nonabelian goldstone bosons in two dimensions

A Polyakov, P.B. Wiegmann (1983)

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Hidden Symmetries of the AdS_5 x S^5 Superstring

Radu Roiban, Joseph Polchinski, Iosif Bena (2003)

Attempts to solve Yang-Mills theory must eventually face the problem of analyzing the theory at intermediate values of the coupling constant. In this regime neither perturbation theory nor the gravity dual are adequate, and one must consider the full string theory in the appropriate background. We suggest that in some nontrivial cases the world sheet theory may be exactly solvable. For the Green-Schwarz superstring on AdS_5 x S^5 we find an infinite set of nonlocal classically conserved charges, of the type that exist in integrable field theories.

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Title: Comptes Rendus Physique

Abbreviated Title: Comptes Rendus Physique

Publisher: Elsevier BV

ISSN (Print): 16310705

Publication date Created: November 2004

Publication date (Print): November 2004

Volume: 5

Issue: 9-10

Pages: 1081-1090

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DOI: 10.1016/j.crhy.2004.09.006

SO-VID: 11059dd1-376d-4da0-8515-8c6e9823ccd9

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http://www.elsevier.com/tdm/userlicense/1.0/

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Semiclassical integrability in AdS/CFT

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Most cited references 28

Gauge Theory Correlators from Non-Critical String Theory

Theory of nonabelian goldstone bosons in two dimensions

Hidden Symmetries of the AdS_5 x S^5 Superstring

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