Gauge-string duality for (non)supersymmetric deformations of N=4 Super Yang-Mills theory

Abstract

We consider a non-supersymmetric example of the AdS/CFT duality which generalizes the supersymmetric exactly marginal deformation constructed in hep-th/0502086. The string theory background we use was found in hep-th/0503201 from the AdS_5 x S5 by a combination of T-dualities and shifts of angular coordinates. It depends on three real parameters gamma_i which determine the shape of the deformed 5-sphere. The dual gauge theory has the same field content as N=4 SYM theory, but with scalar and Yukawa interactions ``deformed'' by gamma_i-dependent phases. The special case of equal deformation parameters gamma_i=gamma corresponds to the N=1 supersymmetric deformation. We compare the energies of semiclassical strings with three large angular momenta to the 1-loop anomalous dimensions of the corresponding gauge-theory scalar operators and find that they match as it was the case in the SU(3) sector of the standard AdS/CFT duality. In the supersymmetric case of equal gamma_i this extends the result of our previous work (hep-th/0503192) from the 2-spin to the 3-spin sector. This extension turns out to be quite nontrivial. To match the corresponding low-energy effective ``Landau-Lifshitz'' actions on the string theory and the gauge theory sides one is to make a special choice of the spin chain Hamiltonian representing the 1-loop gauge theory dilatation operator. This choice is adapted to low-energy approximation, i.e. it allows one to capture the right vacuum states and the macroscopic spin wave sector of states of the spin chain in the continuum coherent state effective action.

arXiv comment43 pages, Latex; v2:Discussion of 0-modes improved in section 2, Appendix B expanded to demonstrate agreement between gauge and string theory for 0-mode fluctuations; references added; v3: Modification to the discussion on the U(1) factor in sec.4.4

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• The general Leigh-Strassler deformation and integrability
• New results in the deformed N=4 SYM theory
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• Worldsheet S-matrix of beta-deformed SYM
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• Pure Spinor Strings in TsT Deformed Background
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• Conformal Invariance = Finiteness and Beta Deformed N=4 SYM Theory
• A review of integrable deformations in AdS/CFT
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• Combinatorial Solution of the Eclectic Spin Chain
• Fast spinning strings on $\eta$ deformed $Ad{S}_5\times S^5$
• Finite-size effects of beta-deformed AdS_5/CFT_4 at strong coupling
• The dual string sigma-model of the SU_q(3) sector
• Semiclassical strings in marginally deformed toric AdS/CFT
• Deformations of flows from type IIB supergravity
• Integrability treatment of AdS/CFT orbifolds
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• On dilatation operator for a renormalizable theory
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• Correlation functions of the ABJM model
• Pulsating Strings in Lunin-Maldacena Backgrounds
• A note on the universality of the Hagedorn behavior of pp-wave strings
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