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

TL;DR

We investigate a three-parameter gamma_i deformation of AdS5×S5 and its non-supersymmetric gauge dual, constructed via TsT, and test the AdS/CFT correspondence in a regime with reduced supersymmetry by comparing energies of semiclassical three-spin strings to one-loop anomalous dimensions of holomorphic three-scalar operators. The authors derive a deformed Landau-Lifshitz action and a twisted SU(3) spin chain, showing exact coincidence of the leading finite-J corrections on both sides through a tailored basis change in the spin-chain Hamiltonian. They identify BPS-like vacua and a gamma-dependent vacuum structure, including a special J_i ∼ γ_i sector, and discuss the implications for stability and conformality in the large-N limit. The work extends known results in the supersymmetric beta deformation to a general non-supersymmetric setting and illustrates how LL-type effective actions can encode string/gauge duality in less-protected regimes.

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.