Research

Matrix Models

Random matrices are a quite broad subject that is still very active. It has applications from number theory, mathematical statistics and physics to neuroscience and finance. My focus has been:

1) The development of a cosmological toy model in two dimensions through a matrix quantum mechanics description. This exploits a well studied duality between Liouville theory or non-critical string theory and matrix models. Together with my collaborators, we applied the aforementioned duality into the description of a Euclidean time orbifold with the idea that the string theory states at the endpoints can capture the physics of Big-Bang, Big-Crunch singularities. In a sense this gave us the possibility to microscopically describe the initial wavefunction of this toy Cosmology.

2) A toy microscopic model of a two dimensional black hole, described by an explicit Hamiltonian of a dynamical Spin-Calogero type. We are currently trying to analyse the thermodynamic and real time properties of this model, with a focus on matching and extending computations that have been performed in Liouville theory. The ultimate goal is to understand puzzles about quantum black holes such as the information paradox and the resolution of a spacelike singularity in a lower dimensional example. See more below.

Black Holes

A very well known paradox related to black hole physics is the so-called information paradox. Stephen Hawking famously showed that black holes radiate with a thermal spectrum. This is hard to square with the basic Unitarity principle of quantum mechanics that demands that pure states cannot evolve into mixed states. Most researchers believe that in fact there is no paradox, all information is stored in the emitted quanta but an explicit calculation that pinpoints the exact mechanism responsible for the preservation of information that falls into the black hole has not yet been performed.

Black Holes and Matrix Models

More recently I have been trying to understand toy models of Black Holes using microscopic Matrix Quantum Mechanics models. The particular model I developed in collaboration with Olga Papadoulaki, includes non-singlet representations sourced by extra dynamical matter fields and in a certain limit has similar physical properties to those of a non-supersymmetric Black Hole in two dimensions (and in an asymptotically flat spacetime).

Such a Black Holes is a lower dimensional version of those that exist in the universe, and the powerful technical machinery of matrix models could allow a deep first principles investigation and resolution of the aforementioned puzzles. This culminates to a synthesis of mathematical ideas such as group representation theory with physical concepts, and could allow for a microscopic understanding of the physics of the Black Hole interior and singularity.

Wormholes

Another exotic type of objects present in gravitational systems are wormholes, ''tunnels'' that connect different regions of space and time. I am particularly interested to understand Euclidean wormholes either through the use of Holography or any other method. The reason is that such objects -in their Euclidean version similar in some respects to instantons and merons of Yang-Mills theory - can in principle affect the gravitational vacuum structure. In the past I have worked on a novel interpretation (using an antipodal identification map) of such solutions as ''holes of nothing'' - regions of space that have been excised - One can imagine interesting effects coming from such a gas of ''bubbles of nothing'' such as a renormalisation of coupling constants - in a sense while the vacuum is full of virtual particles, a bubble of nothing could dilute the vacuum energy potentially resulting in a mechanism able to solve various hierarchy problems -

On the other hand I have been recently working into developing a Holographic interpretation of such solutions. In my recent publications, a detailed bottom up study of several kinds of wormhole solutions was undertaken. In this work we focused on universal features that correlation functions of both local and non-local operators placed on distinct wormhole boundaries should have. In particular these cross-correlation functions of local operators should decay in the UV and have no short distance singularities, while growing strong in the IR. The correlation function of loop operators exhibits a phase transition as one increases the size of the loop, from a configuration that involves exchanges of bulk supergraviton and other perturbative modes to a connected configuration of cylindrical topology. These properties reveal that the holographic dual should be a theory with two sectors that are weakly cross-coupled in the UV and become strongly cross-coupled in the IR with a confining type of behaviour (gapped system). Later on, Mark Van Raamsdonk proposed some concrete microscopic constructions of such systems. With our team we analysed in detail some specific microscopic systems of that kind - QFT's that are coupled by a higher dimensional topological "messenger" QFT, - verifying the results of our previous bottom-up analysis.

The Black Hole S-matrix

My research focused on the S-matrix approach for the description of quantum black holes based on earlier work by Gerard 't Hooft. In this approach one is able to show that strong gravitational backreaction effects (from the point of view of the external observer) cause the ingoing particles to affect the outgoing ones in a precise manner so that the resulting scattering matrix is unitary. Together with my collaborators we found an explicit dynamical quantum mechanical system that results in the same S-matrix, whose Hamiltonian is related to a Dilation operator in a partial wave basis. Moreover this construction pinpoints where to find the lost information. One has to look at antipodal correlations between asymptotic Hawking quanta. This line of research looks really exciting and the next step is to incorporate all the Standard Model forces and particles into the picture.

In more recent work together with my collaborators, I motivated a local form of this identification that takes into account the symmetries of the Dilation Hamiltonian and the phase space structure. This provides a natural condition for a discretisation of the black hole spectrum, that is shown to coincide with the zeros of the Riemann zeta and Dirichlet beta functions. It strengthens the proposal that the proposed quantum Hamiltonian captures the dynamics of modes on a Schwarzschild black hole, given the rich chaotic spectrum. It also explains why the spectrum appears to be erratic despite the unitarity of the scattering matrix.