Talks

We investigate a simple theory where Baryon number (B) and Lepton number (L) are local gauge symmetries. In this theory B and L are on the same footing and the anomalies are cancelled by adding a single new fermionic generation. There is an interesting realization of the seesaw mechanism for neutrino masses. Furthermore there is a natural suppression of flavour violation in the quark and leptonic sectors since the gauge symmetries and particle content forbid tree level flavor changing neutral currents involving the quarks or charged leptons. Also one finds that the stability of a dark matter candidate is an automatic consequence of the gauge symmetry. Some constraints and signals at the Large Hadron Collider are briefly discussed.

Topological phases in spin systems are exciting frontiers of research with intimate connections to quantum coding theory. However, there is a disconnection between quantum codes and the idea of topology, in the absence of geometry and physical realizability. Here, we introduce a toy model, in which quantum codes are constrained to not only have a local geometric description, but also have translation and scale symmetries. These additional physical constraints enable us to assign topologically invariant properties to geometric shapes of logical operators of the code. Topological phases of the model are analyzed by geometrically classifying logical operators. The classification scheme also has topologically universal properties which are invariant under local unitary transformations and local perturbations, and may explain how global symmetries of a system Hamiltonian give rise to topological phases in correlated spin systems.

I will present recent numerical results obtained in collaboration with Frans Pretorius that describe head-on collisions of two solitons coupled to the general relativistic gravitational field and boosted to ultra relativistic energies. The calculations show, for the first time, that at sufficiently high energies such a collision leads to black hole formation, consistent with hoop conjecture arguments. This implies that the non-linear gravitational interaction between the kinetic energy of the solitons results in gravitational collapse, and the arguments for black hole formation in super-Planck scale particle collisions are robust. I will also speculate on the nature of the threshold of black hole formation in the model.