Gauge-string duality for (non)supersymmetric deformations of image super-Yang–Mills theory Original Research Article

We consider a nonsupersymmetric example of the AdS/CFT duality which generalizes the supersymmetric exactly marginal deformation constructed in . The string theory background we use was found in from the image by a combination of T-dualities and shifts of angular coordinates. It depends on three real parameters image which determine the shape of the deformed 5-sphere. The dual gauge theory has the same field content as image SYM theory, but with scalar and Yukawa interactions “deformed” by image-dependent phases. The special case of equal image corresponds to the image 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 image sector of the standard AdS/CFT duality. In the supersymmetric case of equal image this extends the result of our previous work () 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.