Triangle Seminars

Abstract:
I'll explain a new way of looking at 4d supergravity –- as a theory of holomorphic maps into Penrose's twistor space. Allowing twistor space to have N fermionic directions, the theory is anomaly free when N=8. Via the Penrose transform, the vertex operators correspond to an N=8 Einstein supergravity multiplet. Conformal symmetry is explicitly broken by the presence of the infinity twistor in the BRST operator. I will show how to compute the complete classical S-matrix from worldsheet correlation functions, and interpret these amplitudes geometrically.

Abstract:
Compactifications of string theory on Calabi-Yau threefolds lead to supersymmetric four-dimensional vacua with unstable moduli. In order to stabilise these moduli, one may introduce background fluxes in the compact 6-manifold. However, such fluxes backreact on the internal geometry so that the Calabi-Yau condition is broken and a weaker condition of reduced structure group is imposed instead. In contrast to the vast number of Calabi-Yau manifolds, few manifolds with the relevant structure group have been constructed, and this lack of examples has left important properties of flux compactifications in obscurity.
In this talk, I will report on recent progress in the construction of SU(3) structures on 6-dimensional smooth compact toric varieties (SCTVs). I will review the topological criterium for the existence of an SU(3) structure on a 6-manifold, which can be fulfilled on an infinite class of SCTVs. Since in string vacua the torsion of the SU(3) structure are constrained, I will then present a method to explicitly construct the SU(3) structure and compute its torsion. I will discuss when parametric choices can be made to tune the torsion classes, and illustrate the construction with several examples.

Abstract:
How many H2O molecules are needed to form water? While the precise answer is not known, it is clear that the answer should be a finite number rather than infinity. We revisit with care the ideal Bose gas confined in a cubic box which is discussed in most statistical physics textbooks. We show that the isobar of the ideal gas zigzags on the temperature-volume plane featuring a `boiling-like' discrete phase transition, provided the number of particles is equal to or greater than a particular value: 7616. This demonstrates for the first time how a finite system can feature a mathematical singularity and realize the notion of `Emergence', without resorting to the thermodynamic limit.
ref: arXiv:1310.5580

Abstract:
Over the last five years, the gauge/gravity correspondence has been applied to describe quantum critical systems at finite density. The simplest model to consider is Einstein-Maxwell gravity, and the ground state of the system is described by Reissner-Nordstrom black hole where all the charge is carried by the black hole. However, it turns out that this solution is unstable to the formation of both fermionic and bosonic matter, corresponding in the dual field theory to the creation of a Fermi surface and the onset of superconductivity, respectively. We consider Einstein-Maxwell system coupled to a perfect fluid of charged fermions and a charged scalar field. In addition to the black hole, electron star and holographic superconductor solutions, we find new asymptotically AdS 4 solutions, dual to 2+1 CFTs at zero temperature and finite chemical potential, which contain both scalar hair and an electron star. We compute the free energy and show that these new solutions are thermodynamically favoured when they exist. Moreover, we find evidence for a continuous phase transition between the holographic superconductor and the new solutions.