Particle theory

Abstract:

We consider a class of multi-matrix models with an action which is O(D) invariant, where D is the number of NxN Hermitian matrices X_\mu, \mu=1,...,D. The action is a function of all the elementary symmetric functions of the matrix $T_{\mu\nu}=Tr(X_\mu X_\nu)/N$. We address the issue whether the O(D) symmetry is spontaneously broken when the size N of the matrices goes to infinity. The phase diagram in the space of the parameters of the model reveals the existence of a critical boundary where the O(D) symmetry is maximally broken.

Abstract:

A satisfactory theory of quantum gravity will very likely require modification of our classical perception of space-time, perhaps by giving it a 'foamy' structure at scales of order the Planck length. This is expected to modify the propagation of photons and other relativistic particles such as neutrinos, such that they will experience a non-trivial refractive index even in vacuo. The implied spontaneous violation of Lorentz invariance may also result in alterations of kinematical thresholds for key astrophysical processes involving high energy cosmic radiation. We discuss experimental probes of these possible manifestations of the fundamental quantum nature of space-time using observations of distant astrophysical sources such as gamma-ray bursts and active galactic nuclei.