Scientific Series

I will describe our recent work on a new topological phase of matter: topological Weyl semimetal. This phase arises in three-dimensional (3D) materials, which are close to a critical point between an ordinary and a topological insulator. Breaking time-reversal symmetry in such materials, for example by doping with sufficient amount of magnetic impurities, leads to the formation of a Weyl semimetal phase, with two (or more) 3D Dirac nodes, separated in momentum space. Such a topological Weyl semimetal possesses chiral edge states and a finite Hall conductivity, proportional to the momentum-space separation of the Dirac nodes, in the absence of any external magnetic field. Weyl semimetal demonstrates a qualitatively different type of topological protection: the protection is provided not by the bulk band gap, as in topological insulators, but by the separation of gapless 3D Dirac nodes in momentum space. I will describe a simple way to engineer such materials using superlattice heterostructures, made of thin films of topological insulators. References: arXiv:1110.1089; Phys. Rev. Lett. 107, 127205 (2011); Phys. Rev. B 83, 245428 (2011)."

In this talk I will give an overview of localization and some of its applications for QFTs in three dimensions. I will start by reviewing the localization procedure for N=2 supersymmetric gauge theories in three dimensions on S^3. I will then describe some of the applications to field theory dualities and to holography, and the possibility of extracting information about RG fixed points from the localized partition function.

It is my contention that non-commutative geometry is really "ordinary geometry" carried out in a non-commutative logic. I will sketch a specific project, relating groupoid C*-algebras to toposes, by means of which I hope to detect the nature of this non-commutative logic.

I briefly introduce the recently introduced idea of relativity of locality, which is a consequence of a non-flat geometry of momentum space. Momentum space can acquire nontrivial geometrical properties due to quantum gravity effects. I study the relation of this framework with noncommutative geometry, and the Quantum Group approach to noncommutative spaces. In particular I'm interested in kappa-Poincaré, which is a Quantum Group that, as shown by Freidel and Livine, in the 1+1D case emerges as the symmetry of effective field theory coupled with quantum gravity, once that the gravitational degrees of freedom are integrated out. I'm interested in particular in the Lorentz covariance of this model which is present, but is realized in a nontrivial way. If I still have time, I'll then speak about an under-course general study of the Lorentz covariance of Relative Locality models.

We investigate the use of the embedding formalism and the Mellin transform in the calculation of tree-level conformal correlation functions in $AdS$/CFT. We evaluate 5- and 6-point Mellin amplitudes in $phi^3$ theory and even a 12-pt diagram in $phi^4$ theory, enabling us to conjecture a set of Feynman rules for scalar Mellin amplitudes. We also show how to use the same combination of Mellin transform and embedding formalism for amplitudes involving fields with spin. The complicated tensor structures which usually arise can be written as certain operators acting as projectors on much simpler index structures - essentially the same ones appearing in a flat space amplitude. Using these methods we are able to evaluate a four-point current diagram with current exchange in Yang-Mills theory.

The development of virial mass estimates for the central black hole using one quasar spectrum has allowed a dramatic improvement in our understanding of supermassive black hole evolution. I will describe several new puzzles arising from the combination of virial masses with luminosity and redshift measurements, many of which are inconsistent with our current understanding of quasar evolution. I will also describe a new class of quasars that does not appear to fit easily into current models for quasar accretion.

The Standard Model is currently the theory which describes the most fundamental constituents of matter and the forces which govern their interactions. Since the start-up of the LHC accelerator, the ATLAS detector has collected sufficient data to allow tests of this theory at the smallest distance scales ever probed. The objective is to find significant deviations between the observed data and the Standard Model predictions, revealing the existence of new phenomena. For example, some theories in which the universe has more than 4 space-time dimensions predict that LHC collisions could produce gravitons - the particles responsible for the gravitational interaction. Such events would feature a single jet of hadronic particles in the detector and a large amount of

The study of the anisotropies in the cosmic microwave background radiation over the past two decades has provided us with important information about the early universe. In particular, there is strong evidence that these anisotropies were generated long before the cosmic microwave radiation was emitted. The most commonly studied idea is that they originated as quantum fluctuations during a period of inflation. In addition to a spectrum of scalar perturbations consistent with the one that has been observed, inflation also predicts the presence of gravitational waves. These might be observable in the polarization of the cosmic microwave background. An observation of this signal would indicate that the inflaton must have traversed a super-Planckian distance. Realizing this in string theory has been challenging. I will describe the basic ingredients for a string theoretic setup in which the inflaton can move over a super-Planckian distance, leading to an observable gravitational wave signal within string theory. In addition to an observable tensor signal, the model may also lead to other interesting signatures which I will discuss such as modulations in the power spectrum of scalar perturbations, interesting shapes of non-Gaussianities, and possibly the formation of oscillons at the end of inflation.

Topology has many different manifestations in condensed matter physics. Real space examples include topological defects such as vortices, while momentum space ones include topological band structures and singularities in the electronic dispersion. In this talk, I will focus on two examples. The first is that of a vortex in a topological insulator that is doped into the superconducting state. This system, we find, has Majorana zero modes and thus, is a particularly simple way of obtaining these states. We derive general existence criteria for vortex Majorana modes and find that existing systems like Cu-doped Bi2Se3 fulfill them. In the process, we discover a rare example of a topological phase transition within a topological defect (the vortex) at the point when the criteria are violated. The second example is that of Weyl semimetals, which are three-dimensional analogs of graphene. Interestingly, the Dirac nodes here are topological objects in momentum space and are associated with peculiar Fermi-arc surface states. We discuss charge transport in these materials in the presence of interactions or disorder, and find encouraging agreement with existing experimental data.