The center for Theoretical Physics (CPHT) at Ecole Polytechnique gathers research scientists working in diverse domains of fundamental and applied Physics. The overall coherence is assured by the corpus of common, transposable, mathematical and numerical methods.
CPHT is a joint research unit of CNRS and Ecole Polytechnique, and has a partnership with the Collège de France. His director is Jean-René Chazottes, Senior Researcher at CNRS.
CPHT is on the campus of Ecole Polytechnique, buildings 5 and 6. The reception offices are located in building 6 , offices 06.1046 and 06.1045.

Postal Address :
Ecole Polytechnique 
91128 Palaiseau cedex 

Secretary phone number : 01 69 33 42 01 (from abroad: +33 169 334 201)

Write an email to someone at CPHT :  :



Sabine Harribey soutiendra publiquement ses travaux de thèse le 17 juin 2022 à l'INRIA (bâtiment Alan Turing), salle Gilles Kahn.

Titre de la thèse : Renormalization in tensor field theory and the melonic fixed point

Participer à la réunion Zoom pour la soutenance de thèse :
ID de réunion : 899 4655 2020

Co-directeurs de thèse : Razvan Gurau, Dario Benedetti et Christoph Kopper

Membres du jury :
- Holger Gies (Université Friedrich-Schiller de Jena) Rapporteur
- Grigory Tarnopolsky (Carnegie Mellon University) Rapporteur
- Matthias Bartelmann (Université d’Heidelberg)
- Lauriane Chomaz (Université d’Heidelberg)
- Vincent Rivasseau (Université Paris-Saclay)

Abstract: This thesis focuses on the study of the renormalization group flow in tensor field theories. Its first part considers a quartic tensor model with O(N)^3 symmetry and long-range propagator. The existence of a non-perturbative fixed point in any d at large N is established. We found four lines of fixed points parametrized by the so-called tetrahedral coupling. One of them is infrared attractive, strongly interacting and gives rise to a new kind of conformal field theories, called melonic CFTs. This melonic CFT is then studied in more details. We first compute dimensions of bilinears and operator product expansion coefficients at the fixed point. The results are consistent with a unitary CFT at large N. We then compute 1/N corrections to the fixed point. At next-to-leading order, the line of fixed points collapses to one fixed point. However, the corrections are complex and unitarity is broken at next-to-leading order. Finally, the F-theorem is investigated for this model. This theorem states that the free energy of a CFT on the sphere in dimension 3 decreases along the renormalization group flow. We show that our model respects this theorem. The next part of the thesis investigates sextic tensor field theories in rank 3 and 5. In rank 3, we found two infrared stable real fixed points in short range and a line of infrared stable real fixed points in long range. Surprisingly, the only fixed point in rank 5 is the Gaussian one. For the rank 3 model, in the short-range case, we still find two infrared stable fixed points at next-to-leading order. However, in the long-range case, the corrections to the fixed points are non-perturbative and hence unreliable: we found no precursor of the large N fixed point.  The last part of the thesis investigates the class of model exhibiting a melonic large N limit. Indeed, this limit was lacking for models with ordinary tensor representations of O(N) and Sp(N), such as symmetric traceless or antisymmetric ones. Recently, it was proven that models with tensors in an irreducible representation of O(N) or Sp(N) in rank 3 indeed admit a large N limit. This proof is here extended in rank 5. This generalization relies on recursive bounds derived from a detailed combinatorial analysis of Feynman graphs involved in the perturbative expansion of our model.



Mini-conference on Condensed Matter, Fields and Gravity

June 10th, 2022 10:00 am - 15:30 pm

at CPHT, room Louis Michel, CPHT, Ecole Polytechnique

Schedule and speakers :

10am-10:45am: Costas Bachas (LPTENS, Paris, France)

10:45am-11:15am: Coffee break

11:15am:12pm: Chris Herzog (King's College, London, UK)

12pm-12:45pm: Kristan Jensen (University of Victoria, Canada)

12:45pm-2pm: Lunch

2pm:2:45pm: Karl Landsteiner (UAM, Madrid, Spain)

2:45pm-3:30pm: Jan Zaanen (Leiden University, the Netherlands)

3:30pm: Coffee break

4:00pm-4:45pm: Ayan Mukhopadhyay (IIT Madras, India)

Titles and Abstracts

Organized by Blaise Goutéraux (CPHT)



The 4th CPHT Young Researchers Seminar will be held on May 6, 2022 at 3:00 p.m. in the Louis Michel Conference Room with two presentations given by :

Mohamed Rekhis : Shear Alfvén Waves in toroidally confined plasmas

Erik Linnér : Competing collective fluctuations in interacting electron systems

The seminar will be followed by a high tea.



Jean-Pierre Fest : a scientific symposium dedicated to Jean-Pierre Derendinger on the occasion of his 67th birthday

19 and 20 april 2022, Ecole normale supérieure

organized by Ignatios Antoniadis, Adel Bilal, Marios Petropoulos

More information : here



Second announcement: registration for "Quantum gravity, random geometry and holography" From January 9th to February 17th, 2023, at the Institut Henri Poincaré (Paris)

Important: the deadline for financial support requests is June 15th, 2022

Program : The thematic six-weeks program will include two workshops (weeks 2 and 5), introductory lectures (weeks 1 and 4), two general public lectures (to be announced), and more (informal gatherings and seminars).

Organizing committee : John Barrett (University of Nottingham), Dario Benedetti (CNRS, École Polytechnique), Joseph Ben Geloun (Université Sorbonne Paris Nord), Renate Loll (Radboud University Nijmegen)

More information : here