All loop BMN state energies from matrices

DAVID BERENSTEIN; DIEGO H. CORREA; SAMUEL E. VAZQUEZ

JOURNAL OF HIGH ENERGY PHYSICS - (Online)

Institute of Physics

Lugar: Trieste, Italia; Año: 2006 vol. 02 p. 1 - 16

1029-8479

We study a quantum corrected SO(6) invariant matrix quantum mechanics obtained from the s-wave modes of the scalars of N = 4 SYM on S3. For commuting matrices, this model is believed to describe the 1/8 BPS states of the full SYM theory. In the large-N limit the ground state corresponds to a distribution of eigenvalues on a S5 which we identify with the sphere on the dual geometry AdS5 × S5. We then consider non-BPS excitations by studying matrix perturbations where the off-diagonal modes are treated perturbatively. To a first approximation, these modes can be described by a free theory of ``string bits" whose energies depend on the diagonal degrees of freedom. We then consider a state with two string bits and large angular momentum J on the sphere. In the large J limit we use a simple saddle point approximation to show that the energy of these states coincides precisely with the BMN spectrum to all orders in the ´t Hooft coupling. We also find some new problems with the all loop Bethe Ansatz conjecture of the N = 4 SYM planar spin chain model.