The Supergravity Dual of the BMN Matrix Model

We propose type IIA supergravity solutions dual to the 1/2 BPS vacua of the BMN matrix model. These dual solutions are analyzed using the Polchinski-Strassler method and have brane configurations of concentric shells of D2 branes (or NS5 branes) with various radii and D0 charge. These branes can be viewed as polarized from $N$ D0 branes by a transverse R-R magnetic 6-form flux and an NS-NS 3-form flux. In the region far from branes, the solutions reduce to perturbation around the near horizon geometry of $N$ D0 branes, by turning on these R-R and NS-NS fluxes, which are dual to the deformation of the BFSS matrix model by adding mass terms and the Myers term. The solutions with these additional fluxes preserve 16 supersymmetries. We also briefly discuss these fluxes in the possible supergravity duals of M(atrix) theories on less supersymmetric plane-waves.Comment: 33 pages, LaTe

Relation between large dimension operators and oscillator algebra of Young diagrams

The operators with large scaling dimensions can be labelled by Young diagrams. Among other bases, the operators using restricted Schur polynomials have been known to have a large $N$ but nonplanar limit under which they map to states of a system of harmonic oscillators. We analyze the oscillator algebra acting on pairs of long rows or long columns in the Young diagrams of the operators. The oscillator algebra can be reached by a Inonu-Wigner contraction of the $u(2)$ algebra inside of the $u(p)$ algebra of $p$ giant gravitons. We present evidences that integrability in this case can persist at higher loops due to the presence of the oscillator algebra which is expected to be robust under loop corrections in the nonplanar large $N$ limit.Comment: 21 page

AdS backgrounds and induced gravity

In this paper we look for AdS solutions to generalised gravity theories in the bulk in various spacetime dimensions. The bulk gravity action includes the action of a non-minimally coupled scalar field with gravity, and a higher-derivative action of gravity. The usual Einstein-Hilbert gravity is induced when the scalar acquires a non-zero vacuum expectation value. The equation of motion in the bulk shows scenarios where AdS geometry emerges on-shell. We further obtain the action of the fluctuation fields on the background at quadratic and cubic orders.Comment: 17 pages. Journal versio

Detecting topology change via correlations and entanglement from gauge/gravity correspondence

We compute a momentum space version of the entanglement spectrum and entanglement entropy of general Young tableau states, and one-point functions on Young tableau states. These physical quantities are used to measure the topology of the dual spacetime geometries in the context of gauge/gravity correspondence. The idea that Young tableau states can be obtained by superposing coherent states is explicitly verified. In this quantum superposition, a topologically distinct geometry is produced by superposing states dual to geometries with a trivial topology. Furthermore we have a refined bound for the overlap between coherent states and the rectangular Young tableau state, by using the techniques of symmetric groups and representations. This bound is exponentially suppressed by the total edge length of the Young tableau. It is also found that the norm squared of the overlaps is bounded above by inverse powers of the exponential of the entanglement entropies. We also compute the overlaps between Young tableau states and other states including squeezed states and multi-mode entangled states which have similarities with those appeared in quantum information theory.Comment: 48 pages. version in Journal of Mathematical Physic