Talks

Attempts to go beyond the framework of local quantum field theory include scenarios in which the action of external symmetries on the quantum fields Hilbert space is deformed. A common feature of these models is that the quantum group symmetry of their Hilbert spaces induces additional structure in the multiparticle states which in turns reflects a non-trivial momentum-dependent statistics. In certain particular models which might be relevant for quantum gravity the richer structure of the deformed Fock space allows for the possibility of entanglement between the field modes and certain ''planckian'' degrees of freedom invisible to an observer that cannot probe the Planck scale.

An entirely new kind of band insulator was discovered recently. These new electronic states - called "topological insulators" - are fundamentally different from standard band insulators. They are distinguished by the fact that their edges (in the 2D case) or surfaces (in the 3D case) support gapless transport which is extremely robust. In the two dimensional case, topological insulators can be thought of as time reversal invariant analogues of integer quantum Hall states. This analogy is intriguing since integer quantum Hall states are a special case of the far richer class of fractional quantum Hall states. It is natural to wonder: can topological insulators also be generalized? In this talk, I will investigate this question. I will show that, just as in quantum Hall systems, electron interactions allow for a whole new class of states - which we call "fractional topological insulators." These states have excitations with fractional charge and statistics, in addition to protected edge modes.

I consider some of the issues we face in trying to understand dark energy. Huge fluctuations in the unknown dark energy equation of state can be hidden in distance data, so I argue that model-independent tests which signal if the cosmological constant is wrong are valuable. These can be constructed to remove degeneracies with the cosmological parameters. Gravitational effects can play an important role. Even small inhomogeneity clouds our ability to say something definite about dark energy. I discuss how the averaging problem confuses our potential understanding of dark energy by considering the backreaction from density perturbations to second-order in the concordance model: this effect leads to at least a 10\% increase in the dynamical value of the deceleration parameter, and could be significantly higher owing to a UV divergence. Large Hubble-scale inhomogeneity has not been investigated in detail, and could conceivably be the cause of apparent cosmic acceleration. I discuss void models which defy the Copernican principle in our Hubble patch can explain acceleration through inhomogeneous cosmic curvature. These can fit the small scale CMB, and can explain the observed primordial lithium abundances - a niggling 4 or 5 sigma discrepancy in the concordance model. I describe how we can potentially rule out these models, and so provide an important test for the existence of dark energy.

A plethora of Higgsless models have been proposed and we are in the peculiar situation where Fermilab & LHC results will be extremely interesting whether or not the Higgs boson is found. I present here a model where one of the sacred assumption of quantum field theory (renormalizability) is dropped. A precise prescription for the removal of the divergences guarantees both unitarity and predictivity. Interestingly the model is consistent if the Power counting criterion is enforced in a weak form (Weak Power Counting). Among the novel features one notices an extra parameter (the ratio M_W/M_Z) but also a consistent accommodation of the Majorana neutrino mass.

Two-dimensional non-linear sigma models on some supergroup manifolds are conformal field theories whether the action includes a Wess-Zumino term or not. These models are relevant for the worldsheet description of string theory in Anti-de Sitter backgrounds with Ramond-Ramond fluxes. The current algebra is an useful tool to study these theories. In these lectures I will review the construction of the current algebra. Then I will discuss some applications to the computation of the spectrum and integrability.