Dilatation operator and the super Yang-Mills duals of open strings on AdS giant gravitons

Dilatation operator and the super Yang-Mills duals of open strings on AdS giant gravitons

Gustavo A. Canals (Oxford, uk) , Gabriel A. Somma (La Plata U.)
CECS-PHY-066-290, Apr. 2008. 28pp.
e-Print Archive: hep-th/0408127

We study the one-loop anomalous dimensions of the Super Yang-Mills dual operators to open strings ending on AdS giant gravitons. AdS giant gravitons have no upper bound for their angular momentum and we represent them by the contraction of scalar fields, carrying the appropriate R-charge, with a totally symmetric tensor. We represent the open string motion along AdS directions by appending to the giant graviton operator a product of fields including covariant derivatives. We derive a bosonic lattice Hamiltonian that describes the mixing of these excited AdS giants operators under the action of the one-loop dilatation operator of N=4 SYM. This Hamiltonian captures several intuitive differences with respect to the case of sphere giant gravitons. A semiclassical analysis of the Hamiltonian allows us to give a geometrical interpretation for the labeling used to describe the fields products appended to the AdS giant operators. It also allows us to show evidence for the existence of continuous bands in the Hamiltonian spectrum.

We discuss the physical interpretation of a dynamical and inhomogeneous spherically symmetric solution obtained by Fonarev for a scalar field with an exponential potential. There is a single parameter Tw in the solution which can be set to pm1 if it is non-zero, in addition to the steepness parameter lambda in the potential. The spacetime is conformally static and asymptotically flat Friedmann-Robertson-Walker spacetime. The solution reduces to the Friedmann-Robertson-Walker solution for Tw=0. There are two curvature singularities, of which one is a timelike central singularity and the other is a big-bang or big-crunch type singularity. Depending on the parameters, the spacetime can possess a future outer trapping horizon in the collapsing case. Then the solution represents a dynamical black hole in the sense of Hayward although there is a locally naked singularity at the center and no black-hole event horizon. This demonstrates a weak point of the local definition of a black hole in terms of a trapping horizon.

Canals Gustavo Adolfo
Dr.Física Teórica , Ph.D.math.

adolfocanals@educ.ar