String theory dual of the beta-deformed gauge theory

Abstract

We consider the AdS/CFT correspondence between the beta-deformed supersymmetric gauge theory and the type IIB string theory on the Lunin-Maldacena background. Guided by gauge theory results, we modify and extend the supergravity solution of Lunin and Maldacena in two ways. First we make it to be doubly periodic in the deformation parameter, beta -> beta+1 and beta -> beta+tau_0, to match the beta-periodicity property of the dual gauge theory. Secondly, we reconcile the SL(2,Z) symmetry of the gauge theory, which acts on the constant parameters tau_0 and beta, with the SL(2,Z) invariance of the string theory, which involves the dilaton-axion field tau(x). Our modified configuration transforms correctly under the SL(2,Z) of string theory when its parameters are transformed under the SL(2,Z) of the gauge theory. We interpret the resulting configuration as the string theory (rather than supergravity) background which is dual to the beta-deformed conformal Yang-Mills. Finally, we check that our string theory background leads to the IIB effective action which is correctly reproduced by instanton calculations on the gauge theory side, carried out at weak coupling, in the large-N limit, but to all orders in the deformation parameter beta.

arXiv comment18 pages, v3: extended version, comments, clarifications and references added

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Cited by in corpus (9)

• Magnons, Classical Strings and beta-Deformations
• Integrable twists in AdS/CFT
• The Leigh-Strassler Deformation and the Quest for Integrability
• Complex marginal deformations of D3-brane geometries, their Penrose limits and giant gravitons
• Conformal Invariance in the Leigh-Strassler deformed N=4 SYM Theory
• Instanton test of non-supersymmetric deformations of the AdS_5 x S^5
• AdS/CFT Duality for Non-Anticommutative Supersymmetric Gauge Theory
• $T^3$ deformations and $\beta$-deformed geometries
• Dynamical SUSY Breaking and the Beta-Deformation