Sylvain Carrozza

Sylvain Carrozza
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Sylvain Carrozza

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High Energy Physics - Theory (16)
General Relativity and Quantum Cosmology (13)
Mathematics - Combinatorics (2)
Mathematics - Mathematical Physics (1)
Mathematical Physics (1)
Quantum Physics (1)

Publications Authored By Sylvain Carrozza

We prove the renormalizability of a gauge-invariant, four-dimensional GFT model on SU(2), whose defining interactions correspond to necklace bubbles (found also in the context of new large-N expansions of tensor models), rather than melonic ones, which are not renormalizable in this case. The respective scaling of different interactions in the vicinity of the Gaussian fixed point is determined by the renormalization group itself. This is possible because of the appropriate notion of canonical dimension of the GFT coupling constants takes into account the detailed combinatorial structure of the individual interaction terms. Read More

We study the functional renormalization group of a three-dimensional tensorial Group Field Theory (GFT) with gauge group SU(2). This model generates (generalized) lattice gauge theory amplitudes, and is known to be perturbatively renormalizable up to order 6 melonic interactions. We consider a series of truncations of the exact Wetterich--Morris equation, which retain increasingly many perturbatively irrelevant melonic interactions. Read More

After recalling the definition of Grassmann algebra and elements of Grassmann--Berezin calculus, we use the expression of Pfaffians as Grassmann integrals to generalize a series of formulas relating generating functions of paths in digraphs to Pfaffians. We start with the celebrated Lindstr\"om-Gessel-Viennot formula, which we derive in the general case of a graph with cycles. We then make further use of Grassmann algebraic tools to prove a generalization of the results of (Stembridge 1990). Read More

The appearance of linear spaces, describing physical quantities by vectors and tensors, is ubiquitous in all of physics, from classical mechanics to the modern notion of local Lorentz invariance. However, as natural as this seems to the physicist, most computer scientists would argue that something like a "local linear tangent space" is not very typical and in fact a quite surprising property of any conceivable world or algorithm. In this paper, we take the perspective of the computer scientist seriously, and ask whether there could be any inherently information-theoretic reason to expect this notion of linearity to appear in physics. Read More

Grassmann (or anti-commuting) variables are extensively used in theoretical physics. In this paper we use Grassmann variable calculus to give new proofs of celebrated combinatorial identities such as the Lindstr\"om-Gessel-Viennot formula for graphs with cycles and the Jacobi-Trudi identity. Moreover, we define a one parameter extension of Schur polynomials that obey a natural convolution identity. Read More

We provide a non-technical overview of recent extensions of renormalization methods and techniques to Group Field Theories (GFTs), a class of combinatorially non-local quantum field theories which generalize matrix models to dimension $d \geq 3$. More precisely, we focus on GFTs with so-called closure constraint, which are closely related to lattice gauge theories and quantum gravity spin foam models. With the help of recent tensor model tools, a rich landscape of renormalizable theories has been unravelled. Read More

We define in this paper a class of three indices tensor models, endowed with $O(N)^{\otimes 3}$ invariance ($N$ being the size of the tensor). This allows to generate, via the usual QFT perturbative expansion, a class of Feynman tensor graphs which is strictly larger than the class of Feynman graphs of both the multi-orientable model (and hence of the colored model) and the $U(N)$ invariant models. We first exhibit the existence of a large $N$ expansion for such a model with general interactions. Read More

Building on an analogy with ordinary scalar field theories, an epsilon expansion for rank-3 tensorial group field theories with gauge invariance condition is introduced. This allows to continuously interpolate between the dimension four group SU(2) X U(1) and the dimension three SU(2). In the first situation, there is a unique marginal 4-valent coupling constant, but in contrast to ordinary scalar field theory this model is asymptotically free. Read More

This article provides a Wilsonian description of the perturbatively renormalizable Tensorial Group Field Theory introduced in arXiv:1303.6772 [hep-th] (Commun. Math. Read More

In this thesis, we study the structure of Group Field Theories (GFTs) from the point of view of renormalization theory. Such quantum field theories are found in approaches to quantum gravity related to Loop Quantum Gravity (LQG) on the one hand, and to matrix models and tensor models on the other hand. They model quantum space-time, in the sense that their Feynman amplitudes label triangulations, which can be understood as transition amplitudes between LQG spin network states. Read More

Group field theories have recently been shown to admit a 1/N expansion dominated by so-called `melonic graphs', dual to triangulated spheres. In this note, we deepen the analysis of this melonic sector. We obtain a combinatorial formula for the melonic amplitudes in terms of a graph polynomial related to a higher dimensional generalization of the Kirchhoff tree-matrix theorem. Read More

We address in this paper the issue of renormalizability for SU(2) Tensorial Group Field Theories (TGFT) with geometric Boulatov-type conditions in three dimensions. We prove that tensorial interactions up to degree 6 are just renormalizable without any anomaly. Our new models define the renormalizable TGFT version of the Boulatov model and provide therefore a new approach to quantum gravity in three dimensions. Read More

We tackle the issue of renormalizability for Tensorial Group Field Theories (TGFT) including gauge invariance conditions, with the rigorous tool of multi-scale analysis, to prepare the ground for applications to quantum gravity models. In the process, we define the appropriate generalization of some key QFT notions, including: connectedness, locality and contraction of (high) subgraphs. We also define a new notion of Wick ordering, corresponding to the subtraction of (maximal) melonic tadpoles. Read More

We use a reformulation of topological group field theories in 3 and 4 dimensions in terms of variables associated to vertices, in 3d, and edges, in 4d, to obtain new scaling bounds for their Feynman amplitudes. In both 3 and 4 dimensions, we obtain a bubble bound proving the suppression of singular topologies with respect to the first terms in the perturbative expansion (in the cut-off). We also prove a new, stronger jacket bound than the one currently available in the literature. Read More

Through the question of singular topologies in the Boulatov model, we illustrate and summarize some of the recent advances in Group Field Theory. Read More

Based on recent work on simplicial diffeomorphisms in colored group field theories, we develop a representation of the colored Boulatov model, in which the GFT fields depend on variables associated to vertices of the associated simplicial complex, as opposed to edges. On top of simplifying the action of diffeomorphisms, the main advantage of this representation is that the GFT Feynman graphs have a different stranded structure, which allows a direct identification of subgraphs associated to bubbles, and their evaluation is simplified drastically. As a first important application of this formulation, we derive new scaling bounds for the regularized amplitudes, organized in terms of the genera of the bubbles, and show how the pseudo-manifolds configurations appearing in the perturbative expansion are suppressed as compared to manifolds. Read More