Scientific Series

Tensor models appear as the higher dimensional extension of the so-called matrix models describing 2D quantum gravity through the sum over triangulations of surfaces. In the light of the recent $1/N$ expansion for these tensor models, we uncover a new class of tensor models for 4D and 3D gravity which are renormalizable at all orders of perturbation theory. An overview of two papers, [arXiv:1111.4997 [hep-th]] and [arXiv:1201.0176 [hep-th]], on the renormalization of these tensor models and their beta function will be given.

Group field theories show up as a higher dimensional generalization of matrix models in background independent approaches to quantum gravity.
Their Feynman expansion generates simplicial complexes of all topologies weighted by spin foam amplitudes.
In this talk, we will present a dual formulation of these theories as non-commutative quantum fields theories, whose variables have a clear interpretation in terms of simplicial geometry. We will show that it gives a geometrically clear ways to define spin foam models for gravity which can be cast as

Recent years have seen a renewed interest, both theoretically and experimentally, in the search for topological states of matter. On the theoretical side, while much progress has been achieved in providing a general classification of non-interacting topological states, the fate of these phases in the presence of strong interactions remains an open question. The purpose of this talk is to describe recent developments on this front. In the first part of the talk, we will consider, in a scenario with time-reversal symmetry breaking, dispersionless electronic Bloch bands (flatbands) with non-zero Chern number and show results of exact diagonalization in a small system at 1/3 filling that support the existence of a fractional quantum Hall state in the absence of an external magnetic field. In the second part of the talk, we will discuss strongly interacting electronic phases with time-reversal symmetry in two dimensions and propose a candidate topological field theory with fractionalized excitations that describes the low energy properties of a class of time-reversal symmetric states.

Two uncertainties define the prevailing attitude toward the LHC: uncertainty about what new physics it may find (if any); together with dissatisfaction with the "technical naturalness" arguments which (when applied to the hierarchy problem) help suggest what it should be looking for. The dissatisfaction arises because of a wide-spread despair about finding a technically natural solution to the cosmological constant problem, despite much effort spent seeking it. In this talk I describe a mechanism within supersymmetric extra-dimensional theories that allows the low-energy effective cosmological constant naturally to be of order the Kaluza-Klein scale. If this is the solution to the cosmological constant problem, then it requires extra dimensions that are both very supersymmetric and large enough to be relevant to the LHC (with the - so far successful - prediction that no MSSM particles will be discovered there, despite the low-energy supersymmetry)

I will discuss cosmological, astrophysical and collider constraints on thermal dark matter with mass in the range 1 MeV to 10 GeV. CMB observations can be evaded if the DM relic density is sufficiently asymmetric, while collider constraints generally require sufficiently light mediators. These light mediators can give rise to significant DM self-interactions, and I will describe bounds on such interactions from dark matter halo shapes. Finally, I will describe how these constraints map onto the parameter space of DM-electron and DM-nucleon scattering cross sections for direct detection.

Quantum field theory provides the framework for the Standard Model of particle physics and plays a key role in many areas of physics. However, calculations are generally computationally complex and limited to weak interaction strengths. I shall describe a polynomial-time algorithm for computing, on a quantum computer, relativistic scattering amplitudes in massive scalar quantum field theories. The quantum algorithm applies at both weak and strong coupling, achieving exponential speedup over known classical methods at high precision or strong coupling. The study of such quantum algorithms may also help us learn more about the nature and foundations of quantum field theory itself.

We propose that the fermionic superpartner of a weak-scale Goldstone boson can be a nat- ural WIMP candidate. The p-wave annihilation of this `Goldstone fermion' into pairs of Gold- stone bosons automatically generates the correct relic abundance, whereas the XENON100 direct detection bounds are evaded due to suppressed couplings to the Standard Model. Further, it is able to avoid indirect detection constraints because the relevant s-wave annihi- lations are small. The interactions of the Goldstone supermultiplet can induce non-standard Higgs decays and novel collider phenomenology.

To study the continuum limit of a microscopic model of gravity we need microscopic observables that have a clear interpretation in terms of continuum geometry. In general the construction of such observables is notoriously difficult. In the model of causal dynamical triangulations (CDT) it is clear what the microscopic observables are, but at present the only known well-behaved observables with a continuum interpretation are spatial volumes. In this talk I will demonstrate what it takes to go beyond these by introducing the moduli as observables for CDT in 2+1 dimensions with spatial topology of the torus. Measurements of these observables using computer simulations provide valuable clues concerning the effective action describing CDT in the continuum. In particular I will present numerical evidence indicating that the effective kinetic term is well described by a modified Wheeler-De Witt metric like the one appearing in Horava-Lifshitz gravity.

Paul Dirac has been called ‘the first truly modern theoretical physicist’. In the latter part of his life, he was obsessed by the idea that the fundamental laws of nature must have mathematical beauty. This was ‘almost a religion to him’, he said. In this talk, I shall trace the origins of his fascination with this idea (going back to his school education) and question the account he gave of his contribution to quantum mechanics and field theory, which he often said emerged from his aesthetic perspective. I shall also give some insights into the extraordinary character of this man, whom Niels Bohr called ‘the strangest man’ who ever visited his Institute in Copenhagen.