Semidefinite programming algorithm for the quantum mechanical bootstrap.

We present a semidefinite programming algorithm to find eigenvalues of Schrödinger operators within the bootstrap approach to quantum mechanics. The bootstrap approach involves two ingredients: a nonlinear set of constraints on the variables (expectation values of operators in an energy eigenstate), plus positivity constraints (unitarity) that need to be satisfied. By fixing the energy we linearize all the constraints and show that the feasibility problem can be presented as an optimization problem for the variables that are not fixed by the constraints and one additional slack variable that measures the failure of positivity. To illustrate the method we are able to obtain high-precision, sharp bounds on eigenenergies for arbitrary confining polynomial potentials in one dimension.

Can Topology and Geometry be Measured by an Operator Measurement in Quantum Gravity?

In the context of Lin-Lunin-Maldacena geometries, we show that superpositions of classical coherent states of trivial topology can give rise to new classical limits where the topology of spacetime has changed. We argue that this phenomenon implies that neither the topology nor the geometry of spacetime can be the result of an operator measurement. We address how to reconcile these statements with the usual semiclassical analysis of low energy effective field theory for gravity.

Evidence for fast thermalization in the plane-wave matrix model.

We report on a numerical simulation of the classical evolution of the plane-wave matrix model with semiclassical initial conditions. Some of these initial conditions thermalize and are dual to a black hole forming from the collision of D-branes in the plane-wave geometry. In particular, we consider a large fuzzy sphere (a D2-brane) plus a single eigenvalue (a D0 particle) going exactly through the center of the fuzzy sphere and aimed to intersect it. Including quantum fluctuations of the off-diagonal modes in the initial conditions, with sufficient kinetic energy the configuration collapses to a small size. We also find evidence for fast thermalization: rapidly decaying autocorrelation functions at late times with respect to the natural time scale of the system.

Quantizing open spin chains with variable length and giant gravitons in the anti-de Sitter-space/conformal field-theory correspondence.

We study an XXX open spin chain with variable number of sites, where the variability is introduced only at the boundaries. This model arises naturally in the study of giant gravitons in the anti-de Sitter-space/conformal field-theory correspondence. We show how to quantize the spin chain by mapping its states to a bosonic lattice of finite length with sources and sinks of particles at the boundaries. Using coherent states, we show how the Hamiltonian for the bosonic lattice gives the correct description of semiclassical open strings ending on giant gravitons.

Standard model on a D-brane.

We present a consistent string theory model which produces a simple extension of the standard model, consisting of a D3-brane at a simple orbifold singularity. We envision this as a local singularity within a warped compactification. The phenomenology of the model has some novel features. We note that, for the model to be viable, the scale of stringy physics must be in the multi-TeV range. There are natural hierarchies in the fermion spectrum and there are several possible experimental signatures of the model.