Singular topologies in the Boulatov model

Through the question of singular topologies in the Boulatov model, we illustrate and summarize some of the recent advances in Group Field Theory.Comment: 4 pages; proceedings of Loops'11 (May 2011, Madrid); v2: minor modifications matching published versio

Asymptotic safety in three-dimensional SU(2) Group Field Theory: evidence in the local potential approximation

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. This tensorial analogue of the ordinary local potential approximation allows to investigate the existence of non-perturbative fixed points of the renormalization group flow. Our main finding is a candidate ultraviolet fixed point, whose qualitative features are reproduced in all the truncations we have checked (with up to order 12 interactions). This may be taken as evidence for an ultraviolet completion of this GFT in the sense of asymptotic safety. Moreover, this fixed point has a single relevant direction, which suggests the presence of two distinct infrared phases. Our results generally support the existence of GFT phases of the condensate type, which have recently been conjectured and applied to quantum cosmology and black holes.Comment: 43 pages, many figures; v2: minor correction

Large NN limit of irreducible tensor models: O(N)O(N) rank-33 tensors with mixed permutation symmetry

It has recently been proven that in rank three tensor models, the anti-symmetric and symmetric traceless sectors both support a large $N$ expansion dominated by melon diagrams [arXiv:1712.00249 [hep-th]]. We show how to extend these results to the last irreducible $O(N)$ tensor representation available in this context, which carries a two-dimensional representation of the symmetric group $S_3$. Along the way, we emphasize the role of the irreducibility condition: it prevents the generation of vector modes which are not compatible with the large $N$ scaling of the tensor interaction. This example supports the conjecture that a melonic large $N$ limit should exist more generally for higher rank tensor models, provided that they are appropriately restricted to an irreducible subspace.Comment: 17 pages, 7 figure

Flowing in Group Field Theory Space: a Review

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. We review our current understanding of their renormalization group flows, at both perturbative and non-perturbative levels

The 1/N1/N expansion of the symmetric traceless and the antisymmetric tensor models in rank three

We prove rigorously that the symmetric traceless and the antisymmetric tensor models in rank three with tetrahedral interaction admit a $1/N$ expansion, and that at leading order they are dominated by melon diagrams. This proves the recent conjecture of I. Klebanov and G. Tarnopolsky in JHEP 10 (2017) 037 [arXiv:1706.00839], which they checked numerically up to 8th order in the coupling constant.Comment: 40 pages, many figure

Using Grassmann calculus in combinatorics: Lindstr\"om-Gessel-Viennot lemma and Schur functions

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.Comment: 10 pages, contribution to GASCom 2016; v2: minor correction

Melonic phase transition in group field theory

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. Simple bounds on these amplitudes show the existence of a phase transition driven by melonic interaction processes. We restrict our study to the Boulatov-Ooguri models, which describe topological BF theories and are the basis for the construction of four dimensional models of quantum gravity.Comment: 8 pages, 4 figures; to appear in Letters in Mathematical Physic

Autonomía económica y perfiles de gestión en universidades públicas argentinas

Este es un trabajo de tipo exploratorio donde se analiza la evolución económica de las universidades nacionales de gestión estatal durante el periodo 2006 y 2013. Se presenta un estudio cuantitativo a través del cual se analizan comparativamente 36 universidades nacionales de gestión estatal. La evidencia relevada durante el desarrollo de la investigación da cuenta de importantes asimetrías dentro del sistema universitario nacional, las cuales impactarían en las condiciones con que cuentan las universidades para ejercer sus funciones autónomamente. En este sentido, se identifican distintos perfiles de gestión los cuales se definen según el grado de autonomía económica de cada caso. Los resultados indican que, mientras que hay casos que han logrado incrementar considerablemente sus fuentes de financiamientos, hay otros que dependen casi exclusivamente de los aportes del tesoro nacional. Sobre el final del trabajo, surgen nuevos interrogantes que pretenden abrir líneas de investigación que profundicen sobre la naturaleza de las desigualdades entre perfiles y las razones de su evolución disímil.Fil: Hammond, Fernando. Universidad Nacional de Mar del Plata. Facultad de Ciencias Económicas y Sociales; Argentina.Fil: Carrozza, Tomás. Universidad Nacional de Mar del Plata. Facultad de Ciencias Agrarias; Argentina