Article,
Gauge-string duality for (non)supersymmetric deformations of N = 4 super Yang-Mills theory
Nucl. Phys., (2005)
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.
