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

TL;DR

This paper explores a non-supersymmetric deformation of the AdS/CFT duality, comparing semiclassical string energies with gauge theory anomalous dimensions, extending previous supersymmetric results to a more general, non-supersymmetric setting.

Contribution

It introduces a non-supersymmetric deformation of the AdS/CFT correspondence and demonstrates the matching of string energies with gauge theory dimensions in this new context.

Findings

Semiclassical string energies match 1-loop gauge theory anomalous dimensions.

Extension of previous supersymmetric results to non-supersymmetric deformations.

Special spin chain Hamiltonian captures low-energy gauge theory dynamics.

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.