Publications

My articles, roughly sorted by topic (click on the topic title to see a short description, when available).
For different arrangements and metadata, check inSPIRE or Google Scholar .

On long-range models:

Long-range models are Euclidean field theories whose action has a nonlocal kinetic term, where the ordinary Laplacian is replaced by a fractional power of the Laplacian. They are interesting from a theoretical (and mathematical physics) point of view, as well as from a condensed matter point of view, as their lattice versions describe systems that can be realized experimentally via trapped ions or quantum gases in cavities (see arXiv:2109.01063 for a review). See the introductions of the papers below for a slightly more detailed but still brief motivation and list of references. Notice that also most of the papers on "QFTs in the melonic large-N limit" (below) deal with long-range models; here I list only work on non-melonic models.

Other recent directions:

On quantum field theories in the melonic large-N limit:

These are quantum (or statistical) field theories whose large-N perturbative expansion is dominated by melonic diagrams. This sets them apart from vector or matrix models (dominated by cactus and planar diagrams, respectively),  and makes their renormalization and fixed points controllable. Therefore, they serve as interesting toy models to explore interacting fixed points of the renormalization group and to apply conformal field theory techniques. The main example of such theories are tensor models (a typical example being theories with a global O(N)^3 invariance), but there are also other models, such as SYK and Amit-Roginsky. It should be said that these tensor models are ordinary field theories on a fixed spacetime and have no direct relation to quantum gravity (except perhaps via holography, as for SYK), unlike the purely combinatorial tensor models (see below).

The thesis for my French Habilitation (HDR) is mainly based on this line of research.


On tensor models as models of random geometry (purely combinatorial field theories in zero dimensions):

These are purely combinatorial models (the random variables have no spacetime dependence, or in other words they are fields on zero dimensional spacetime), whose Feynman  diagrams can be interpreted as simplicial (pseudo-)manifolds, i.e. they generalize to higher dimensional manifolds the relations between matrix models and random triangulations. From this point of view, the large-N melonic dominance corresponds to a branched polymer phase of quantum gravity (as found numerically in dynamical triangulations). Putting aside such interpretation and its geometric constructions, the classification of diagrams in the 1/N expansion that one finds in these models applies also to tensor models on a higher-dimensional spacetime, as the power of N associated to a diagram only depends on the combinatorial tensor structure.

On tensorial group field theory (Kontsevich-type tensor models):

These models can be viewed in at least two different ways. In the first interpretation, they are zero-dimensional random tensor models as above, but with a Gaussian part of the Boltzmann weight having a nontrivial index-dependent covariance, breaking the global symmetry of the interactions. From such a point of view, they can be thought as a tensor generalization of the Kontsevich matrix model. In a second interpretation, one can think of the tensor as a scalar field in momentum space, the tensor indices being the components of momentum (taking discrete values because of compactness of space), and N being a UV cutoff; from this point of view the Gaussian part is rather standard (though sometimes long-range), while the interactions have a peculiar type of non-locality. From this second point of view, it is natural to consider a renormalization group flow of the model with respect to N. Either way, these models find their main motivation as simplified versions of a larger class of quantum gravity models.

On asymptotically safe gravity:

That is, on the conjecture (originally proposed by Steven Weinberg in 1976) that the quantum field theory of gravity is nonperturbatively renormalizable, in the sense that it is defined as a relevant perturbation of a nontrivial (i.e. interacting) UV  fixed point. See the Wikipedia entry for a start.

On renormalization group in various models of gravity, or in field theories on curved background:

These are just some unrelated papers, having in common only the renormalization group perspective :)

On Causal Dynamical Triangulations:

An approach to quantum gravity, defining a regularized path integral in terms of simplicial manifolds, along the old idea of Tullio Regge. In CDT, the edge lengths are fixed, but one sums over all possible gluings of the building blocks, respecting a certain foliation structure. See for example arXiv:1203.3591 for a review.

On quantum group symmetries/non-commutative geometry/DSR:

This goes back to my undergraduate studies, with a brief revival during the beginning of my first postdoc. The main idea at the root of these studies is that quantum gravity effects might manifest themselves at intermediate energies as a deformation of the classical spacetime symmetries, such as k-Poincaré, which is a quantum group deformation of the Poincaré group.