Scientific Series

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.

This talk will deal with a new connection formulation for higher-dimensional (Super)gravity theories and its applications. We will start by reviewing the basic ideas of loop quantum gravity. Next, the derivation of the new connection formulation will be discussed and it will be shown that the quantization methods developed in the context of loop quantum gravity apply. We comment on applications of the framework, focusing on making contact with String theory.

Cold atomic gases in optical lattices are emerging as excellent laboratories for testing models of strongly interacting particles in condensed matter physics. It is possible to tune the interactions, dimensionality, spin, statistics and a host of other variables in a completely disorder free environment. This has opened up unique possibilities of mapping out phase diagrams of quantum models and observing quantum phase transitions for the very first time. I will discuss some of the challenges in this field.

Dualities in physics are well known for their conceptual depth and quantitative predictive power in contexts where perturbation theory is unreliable. They are also remarkable for the staggering arrange of physical problems that exploit them, ranging from the study of confinement and unconventional phases in statistical mechanics and field theory to the unification of the string theory landscape. In this talk I will present a new, completely general approach to dualities that affords a systematic theory of quantum dualities and incorporates classical dualities as well into one unified framework. This new algebraic approach is remarkably successful in extending powerful duality techniques to the context of topologically quantum ordered systems and quantum information processing, and affords a compelling foundation for a general theory of exact dimensional reduction or holographic correspondences. Many systems however display only approximate dimensional reduction, and so I will present general inequalities -some of them based on entanglement- linking quantum systems of different spatial dimensionality. These inequalities provide bounds on the expectation values of observables and correlators that can enforce an effective dimensional reduction. In closing I will discuss some implications for (topological) quantum memories.

Critical theories of gravity are certain higher derivative theories in which parameters are so tuned as to eliminate massive excitations for the spin-2 field. Asymptotically AdS black hole entropy in these theories works out to be zero. We show that such theories arise naturally on the boundary of AdS in the form of counterterms. Such counterterms are derived by demanding cutoff independence of the Euclidean onshell action and black hole entropy. The resummed higher derivative action so obtained can be shown to be critical. Connections with log-CFTs will be discussed. For a specific choice of parameters, these theories turn out to be non-dynamical.

We propose models of symmetric WIMP dark matter in which dark matter annihilations generate the baryon asymmetry. We call this mechanism "WIMPy baryogenesis". This provides a dynamical connection between the late-time abundances of both dark matter and baryons. We construct explicit models of leptogenesis and baryogenesis at the weak scale, and find the "miraculous" result that, for order one couplings and weak scale masses for any new fields, the baryon asymmetry and dark matter relic density from WIMPy baryogenesis match the observed values. We also discuss implications for the LHC and dark matter detection experiments.

General relativity is a covariant theory of two transverse, traceless graviton degrees of freedom. According to a theorem of Hojman, Kuchar, and Teitelboim, modifications of general relativity must either introduce new degrees of freedom or violate the principle of general covariance. In my talk, I will discuss modifications of general relativity that retain the same number of gravitational degrees of freedom, and therefore explicitly break general covariance. Motivated by cosmology, the modifications of interest maintain spatial covariance. Demanding consistency of the theory forces the physical Hamiltonian density to obey an analogue of the renormalization group equation, which encodes the invariance of the theory under flow through the space of conformally equivalent spatial metrics.

Weak topological insulators have an even number of Dirac cones in their surface spectrum and are thought to be unstable to disorder, which leads to an insulating surface. Here we argue that the presence of disorder alone will not localize the surface states, rather, the presence of a time-reversal symmetric mass term is required for localization. Through numerical simulations, we show that in the absence of the mass term the surface always flow to a stable metallic phase and the conductivity obeys a one-parameter scaling relation, just as in the case of a strong topological insulator surface. With the inclusion of the mass, the transport properties of the surface of a weak topological insulator follow a two-parameter scaling form.

The LHC has just concluded this year's proton-proton run at 7 TeV CM energy, producing more than 5fb-1of data. While the full data sample collected by the CMS experiment will be analyzed over the winter, many of the present searches for new physics have been completed with 1-2 fb-1. In this talk we will present the most recent updates on the search analyses in CMS, including the Higgs search, searches for supersymmetry, and a plethora of other BSM models, such as extra dimensions, Z's, W_R, leptoquarks, and more. We'll also show the short-term and longer-term plans of the collider and experiments.

Taking String Theory as a ``theoretical laboratory'', I will present handy expressions for bosonic and fermionic (SUSY) higher-spin Noether currents. I will also describe a class of non-local higher-spin Lagrangian couplings that are generically required by the Noether procedure starting from four-points. The construction clarifies the origin of old problems for these systems and links String Theory to some aspects of Field Theory that go beyond its conventional low energy limit. I will finally discuss how the extension of these results to (A)dS brings about the emergence of minimal-like couplings from higher-derivative ones.

In inflationary theories, single field models are typically considered subject to slow-roll conditions. In this talk I will present current observational constraints on deviations from slow-roll, e.g. bounds coming from strong coupling considerations, scale-dependent non-Gaussianities and the tensor-to-scalar ratio. These constraints still allow significant violations of slow-roll conditions. Focusing on non-Gaussian signals, I will discuss a variety of intriguing observable signatures that can be found for fast-rolling single fields.