Complex marginal deformations of D3-brane geometries, their Penrose limits and giant gravitons

Understand

We apply the Lunin--Maldacena construction of gravity duals to beta-deformed gauge theories to a class of Type IIB backgrounds with U(1)^3 global symmetry, which include the multicenter D3-brane backgrounds dual to the Coulomb branch of N=4 super Yang-Mills and the rotating D3-brane backgrounds dual to the theory at finite temperature and chemical potential.

• After a general discussion, we present the full form of the deformed metrics for three special cases, which can be used for the study of various aspects of the marginally-deformed gauge theories.
• We also construct the Penrose limits of the solutions dual to the Coulomb branch along a certain set of geodesics and, for the resulting PP--wave metrics, we examine the effect of beta-deformations on the giant graviton states.
• We find that giant gravitons exist only up to a critical value of the sigma-deformation parameter, are not degenerate in energy with the point graviton, and remain perturbatively stable.