Search Talks

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 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.

A non-trivial test of the string vs. integrability correspondence is suggested: exact equivalence is established between strings in AdS4 x CP3 and the Gromov-Vieira all-loop integrable chain. To do that, the complete one- and two-magnon sector of each respective theory are calculated. In the single-magnon sector a direct perturbative one-loop calculation proves the validity of the dispersion law coming from the Bethe Ansatz, rather than of the one coming from the semiclassical analysis. In the two-magnon sector the full spectrum of the finite-size corrections has been calculated on the string side by us for the first time, that proves to be identical to the integrable chain spectrum. These results are interpreted by us as a confirmation of the exactness of the conjectured Gromov-Vieira Bethe Ansatz.