## Gauge-string duality for superconformal deformations of N=4 super Yang-Mills theory.

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**Citation: **

*S.A. Frolova, R. Roibanb, and A.A. Tseytlinc., Gauge-string duality for superconformal deformations of N=4 super Yang-Mills theory., Journal of High Energy Physics, 7, 2005, 045*

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**Abstract: **

We analyze in detail the relation between an exactly marginal deformation
of N = 4 SYM | the Leigh-Strassler or \?-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 AdS5 # S5 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 ?nd 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 AdS5 # S5 is part of a larger picture underlying the gauge/gravity duality.

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**Author's Homepage: **

http://people.tcd.ie/frolovs
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**Description: **

PUBLISHED
**Author:**FROLOV, SERGEY

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**Publisher: **

Institute of Physics
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**Type of material: **

Journal Article#####
**Series/Report no: **

Journal of High Energy Physics;7;

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**Availability: **

Full text available#####
**Keywords: **

Mathematics, String Theory, Gauge Theory, Super Yang-Mills theory
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