Erbin, Harold Fırat, Atakan Hilmi

The geometry of 4-string contact interaction of closed string field theory is characterized using machine learning. We obtain Strebel quadratic differentials on 4-punctured spheres as a neural network by performing unsupervised learning with a custom-built loss function. This allows us to solve for local coordinates and compute their associated map...

Rivasseau, Vincent

We construct cumulants up to an arbitrary order of a vector model perturbed by a quartic term. The method we use is the multi-scale loop vertex expansion. We prove their Borel summability in a cardioid of the associated coupling constant.

Bouttier, Jérémie Guitter, Emmanuel Miermont, Grégory

We consider planar maps with three boundaries, colloquially called pairs of pants. In the case of bipartite maps with controlled face degrees, a simple expression for their generating function was found by Eynard and proved bijectively by Collet and Fusy. In this paper, we obtain an even simpler formula for \emph{tight} pairs of pants, namely for m...

Coddens, Gerrit

This is a technical clarifying note consisting of two parts. In the first part we derive the expression for a boost in two representations of the homogeneous Lorentz group, viz. the two-dimensional representation SL(2,C) and the four-dimensional Dirac representation in its Cartan-Weyl form. The derivation is purely algebraic. It uses the developmen...

Martin-Dussaud, Pierre
Published in
General Relativity and Gravitation

Calculations in Loop Quantum Gravity (LQG) and spin-foams theory rely heavily on group theory of SU(2) and SL2(C)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$SL_{2}(...

Galaz, José Kazolea, Maria Rousseau, Antoine

We derive transmission operators for coupling linear Green-Naghdi equations (LGNE) with linear shallow water equations (LSWE) --the heterogeneous case -- or for coupling LGNE with LGNE --the homogeneous case. We derive them from a domain decomposition method (Neumann-Dirichlet) of the linear Euler equations by applying the same vertical-averaging p...

Avohou, Remi C. Geloun, Joseph Ben Dub, Nicolas

$O(N)$ invariants are the observables of real tensor models. We use regular colored graphs to represent these invariants, the valence of the vertices of the graphs relates to the tensor rank. We enumerate $O(N)$ invariants as $d$-regular graphs, using permutation group techniques. We also list their generating functions and give (software) algorith...

Gorsky, Alexander Kazakov, Vladimir Levkovich-Maslyuk, Fedor Mishnyakov, Victor

Using the matrix-forest theorem and the Parisi-Sourlas trick we formulate and solve a one-matrix model with non-polynomial potential which provides perturbation theory for massive spinless fermions on dynamical planar graphs. This is a lattice version of 2d quantum gravity coupled to massive spinless fermions. Our model equivalently describes the e...

Bardenet, Rémi Feller, Alexandre Bouttier, Jérémie Degiovanni, Pascal Hardy, Adrien Rançon, Adam Roussel, Benjamin Schehr, Grégory Westbrook, Christoph I.

Some fifty years ago, in her seminal PhD thesis, Odile Macchi introduced permanental and determinantal point processes. Her initial motivation was to provide models for the set of detection times in fundamental bosonic or fermionic optical experiments, respectively. After two rather quiet decades, these point processes have quickly become standard ...

Hersent, Kilian Mathieu, Philippe Wallet, Jean-Christophe

We review the present status of gauge theories built on various quantum space-times described by noncommutative space-times. The mathematical tools and notions underlying their construction are given. Different formulations of gauge theory models on Moyal spaces as well as on quantum spaces whose coordinates form a Lie algebra are covered, with par...