Scientific Series

During the last couple of years Dupuis, Freidel, Livine, Speziale and Tambornino developed a twistorial formulation for loop quantum gravity.
Constructed from Ashtekar--Barbero variables, the formalism is restricted to SU(2) gauge transformations.
In this talk, I perform the generalisation to the full Lorentzian case, that is the group SL(2,C).
The phase space of SL(2,C) (i.e. complex or selfdual) Ashtekar variables on a spinnetwork graph is decomposed in terms of twistorial variables. To every link there are two twistors---one to each boundary point---attached. The formalism provides a clean derivation of the solution space of the reality conditions of loop quantum gravity.
Key features of the EPRL spinfoam model are perfectly recovered.
If there is still time, I'll scatch my current project concerning a twistorial path integral for spinfoam gravity as well. 

I will explain some recent exact developments in N=2 SUSY gauge theories on 3-sphere and its deformations. I will begin by the analysis of Killing spinors and their generalization which are necessary to construct SUSY theories on curved spaces. Then I will sketch the exact computation of partition function using SUSY localization and present a general formula. Some applications to the physics of M5-branes will also be discussed.

The standard cosmological model posits that the universe is homogeneous and statistically isotropic on its largest scales. However, there is no fundamental reason why these properties have to hold, and in fact they can be broken due to interesting new physics. Moreover, there is some evidence from recent WMAP observations for 'anomalies' - including departures from statistical isotropy - on the largest observable scales. Large-scale structure (LSS) - including the distribution of galaxies in the universe - presents a new frontier in testing statistical isotropy and homogeneity, and we are entering an epoch with orders-of-magnitude improvement in the statistics of LSS. In this talk I first review general tests of statistical isotropy using LSS. I then describe results from research done in collaboration with my student Cameron Gibelyou on testing aspects of the statistical isotropy - in particular, dipolar modulations of the galaxy counts - using existing LSS surveys.

Inflation, a postulated epoch of accelerated expansion in the early universe, has become a principal component of the standard model of cosmology. From a wide variety of initial conditions, inflation produces a nearly homogeneous universe populated by density fluctuations that seed large-scale structure. However, inflation is such a good homogenizer that, once unleashed, in many cases it becomes eternal, ending only within spontaneously nucleated bubbles. In this scenario, our observable universe resides inside one such bubble. Surprisingly, it is possible to perform direct observational tests of eternal inflation. The most dramatic and detectable signatures of eternal inflation arise from the collision between bubbles in the very early universe, which leave an imprint on the cosmic microwave background (CMB) radiation. In this talk, I will motivate and describe the eternal inflation scenario and present the results of a search for the signatures of eternal inflation in CMB data from the Wilkinson Microwave Anisotropy Probe.

Finding the exact, quantum corrected metric on the hypermultiplet moduli space in Type II string compactifications on Calabi-Yau threefolds is still an open problem. We address this issue by relating the quaternionic-Kähler metric on the hypermultiplet moduli space to the complex contact geometry on its twistor space. In this framework, Euclidean D-brane instantons are captured by contact transformations between different patches. We derive those by recasting the previously known A-type D2-instanton corrections in the language of contact geometry, covariantizing the result under electro-magnetic duality, and using mirror symmetry. As a result, we are able to express the effects of all D-instantons in Type II compactifications concisely as a sum of dilogarithm functions.

The emergence of fractal features in the microscopic structure of space-time is a common theme in many approaches to quantum gravity. In particular the spectral dimension, which measures the return probability of a fictitious diffusion process on space-time, provides a valuable probe which is easily accessible both in the continuum functional renormalization group and discrete Monte Carlo simulations of the gravitational action. In this talk, I will give a detailed exposition of the fractal properties associated with the effective space-times of asymptotically safe Quantum Einstein Gravity (QEG). Comparing these continuum results to three-dimensional Monte Carlo simulations, we demonstrate that the resulting spectral dimensions are in very good agreement. This comparison also provides a natural explanation for the apparent conflicts between the short distance behavior of the spectral dimension reported from Causal Dynamical Triangulations (CDT), Euclidean Dynamical Triangulations (EDT), and Asymptotic Safety.

Black holes lead a double life, simultaneously the dark, enigmatic, hairless consequence of general relativity and the powerful engines lurking at the hearts of galaxies with cosmological consequences.

In this talk we discuss a proposed dual matrix formulation of N = 4 Super Yang-Mills on R^4 coupled to 4D Einstein supergravity. We review the evidence accumulated so far in favor of this proposal, which includes a successful match of the symmetries of the continuum theory, and the computation of MHV gluon and graviton scattering amplitudes in terms of matrix model correlators. We also discuss some avenues of ongoing investigation.