Gauge-string duality for superconformal deformations of N=4 Super Yang-Mills theory

Abstract

We analyze in detail the relation between an exactly marginal deformation of N=4 SYM - the Leigh-Strassler or ``beta-deformation'' - and its string theory dual (recently constructed in hep-th/0502086) by comparing energies of semiclassical strings to anomalous dimensions of gauge-theory operators in the two-scalar sector. We stress the existence of integrable structures on the two sides of the duality. In particular, we argue that the integrability of strings in AdS_5 x S^5 implies the integrability of the deformed world sheet theory with real deformation parameter. We compare the fast string limit of the worldsheet action in the sector with two angular momenta with the continuum limit of the coherent state action of an anisotropic XXZ spin chain describing the one-loop anomalous dimensions of the corresponding operators and find a remarkable agreement for all values of the deformation parameter. We discuss some of the properties of the Bethe Ansatz for this spin chain, solve the Bethe equations for small number of excitations and comment on higher loop properties of the dilatation operator. With the goal of going beyond the leading order in the 't Hooft expansion we derive the analog of the Bethe equations on the string-theory side, and show that they coincide with the thermodynamic limit of the Bethe equations for the spin chain. We also compute the 1/J corrections to the anomalous dimensions of operators with large R-charge (corresponding to strings with angular momentum J) and match them to the 1-loop corrections to the fast string energies. Our results suggest that the impressive agreement between the gauge theory and semiclassical strings in AdS_5 x S^5 is part of a larger picture underlying the gauge/gravity duality.

50 pages, Latex; v2:typos corrected, references added, clarifications in sec 8 and Appendix A, a discussion of a rational solution added in section 4.2; v3: minor corrections to coefficients in eq. 2.5, 5.2 and appendix A; v4: minor misprints corrected

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• Deforming field theories with $U(1)\times U(1)$ global symmetry and their gravity duals
• Bethe Ansatz for Quantum Strings
• The Factorized S-Matrix of CFT/AdS
• The Dilatation Operator of N=4 Super Yang-Mills Theory and Integrability
• Lax Pair for Strings in Lunin-Maldacena Background
• Integrable Hamiltonian for Classical Strings on AdS_5 x S^5
• Quantum Consistency of the Superstring in AdS_5 x S^5 Background
• Integrability in QCD and beyond
• Semiclassical relativistic strings in S^5 and long coherent operators in N=4 SYM theory
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• Semiclassical Strings on AdS_5 x S^5/Z_M and Operators in Orbifold Field Theories
• N=2 Super Yang-Mills and the XXZ spin chain

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