# Joseph Ben Geloun

Laboratoire d'Informatique de Paris Nord

Areas of Research:

## Research Interests

My main research interests are on Group Field Theory and Tensor models called henceforth Tensorial Group Field Theories (TGFT's) as approaches for quantum gravity. They can be regarded as theories generalizing Matrix models celebrated in the 80's as successful models
for 2D quantum gravity. TGFT's generate, at the perturbative level, Feynman graphs as simplicial manifolds and therefore provide a realization of a quantum theory for topology in arbitrary dimension. They are very attractive because they offer, within a traditional field-theoretical formalism, one of the most complete framework for a background independent quantum theory of gravity. As a quantum field theory formulated by a functional integral, TGFT's should satisfy some renormalizability conditions that I am investigating.

## Positions Held

• 2008 -2009 National Institute for Theoretical Physics, NITHEP, Stellenbosch, South Africa Post-doc

## Recent Publications

• R. C. Avohou, J Ben Geloun and L. Etera, On terminal forms for topological polynomials for ribbon graphs: The $N$-petal flower,'' to appear in European Journal of Combinatorics (2013) doi 10.1016/j.ejc.2013.08.001; arXiv: 1212.5961 [math.CO].
• J. Ben Geloun and V. Rivasseau, Addendum to 'A Renormalizable 4-Dimensional Tensor Field Theory','' Commun. Math. Phys. 322, 957 (2013) arXiv: 1209.4606 [hep-th].
• J. Ben Geloun and E. R. Livine, Some classes of renormalizable tensor models,'' J. Math. Phys. 54, 082303 (2013) arXiv: 1207.0416 [hep-th].
• J. Ben Geloun and J. R. Klauder, Enhanced quantization on the circle,'' Phys. Scripta 03, 035006 (2013) arXiv: 1206.1180 [math-ph].
• J. Ben Geloun, Two and four-loop beta-functions of rank 4 renormalizable tensor field theories,'' Class. Quant. Grav. 29, 235011 (2012) arXiv: 1205.5513 [hep-th].
• J. Ben Geloun, J. Hnybida, J. R. Klauder, Coherent states for continuous spectrum operators with non-normalizable fiducial states,'' J. Phys. A: Math. Theor. 45, 085301 (2012) arXiv: 1111.6913 [math-ph].
• J. Ben Geloun, Classical Group Field Theory,'' J. Math. Phys. 53, 022901 (2012) arXiv: 1107.3122 [hep-th].
• J. Ben Geloun and D. O. Samary, 3D Tensor Field Theory: Renormalization and One-loop $\beta$-functions,'' Annales Henri Poincare 14, 1599 (2013) arXiv: 1201.0176 [hep-th].
• J. Ben Geloun and V. Rivasseau, A Renormalizable 4-Dimensional Tensor Field Theory,'' Commun. Math. Phys. 318, 69 (2013) arXiv: 1111.4997 [hep-th].
• J. Ben Geloun, Ward-Takahashi identities for the colored Boulatov model,'' J. Phys. A: Math. Theor. 44, 415402 (2011) arXiv: 1106.1847 [hep-th].
• J. Ben Geloun and V. Bonzom, Radiative corrections in the Boulatov-Ooguri tensor model: The 2-point function,'' Int. J. Theor. Phys. 50, 2819 (2011) arXiv: 1101.4294 [hep-th].
• J. Ben Geloun and R. Gurau, Asymptotes in SU(2) Recoupling Theory: Wigner Matrices, $3j$ Symbols, and Character Localization,'' Annales Henri Poincare 12, 77 (2011) arXiv: 1009.5632 [math-ph].
• J. Ben Geloun, R. Gurau and V. Rivasseau, EPRL/FK Group Field Theory,'' EPL 92, 60008 (2010) arXiv: 1008.0354 [hep-th].
• J. Ben Geloun, J. Magnen and V. Rivasseau, Bosonic Colored Group Field Theory,'' Eur. Phys. J. C 70, 1119 (2010) arXiv: 0911.1719 [hep-th].
• J. Ben Geloun, T. Krajewski, J. Magnen and V. Rivasseau, Linearized Group Field Theory and Power Counting Theorems,'' Class. Quant. Grav. 27, 155012 (2010) arXiv: 1002.3592[hep-th].
• J. Ben Geloun, On the finite amplitudes for open graphs in Abelian dynamical colored Boulatov-Ooguri models,'' arXiv: 1307.8299 [hep-th].
• J. Ben Geloun and S. Ramgoolam, Counting Tensor Model Observables and Branched Covers of the 2-Sphere,'' arXiv: 1307.6490 [hep-th].
• J. Ben Geloun and J. R. Klauder, The finite and large-$N$ behaviors of independent-value matrix models,'' arXiv: 1306.4403 [hep-th].
• J. Ben Geloun, Renormalizable Models in Rank $d\geq 2$ Tensorial Group Field Theory,'' arXiv: 1306.1201 [hep-th].
• Remi C. Avohou, Joseph Ben Geloun, Mahouton N. Hounkonnou A Polynomial Invariant for Rank 3 Weakly-Colored Stranded Graph,'' arXiv: 1301.1987[math.CO]
• J. Ben Geloun Enhanced Quantization: The particle on the circle,'' Contribution to the XXIXth International Colloquium on Group-Theoretical Methods in Physics, Nankai, China, August 20-26, 2012; arXiv: 1210.5492 [math-ph].
• J. Ben Geloun, Asymptotic Freedom of Rank 4 Tensor Group Field Theory,'' Contribution to the XXIXth International Colloquium on Group-Theoretical Methods in Physics, Nankai, China, August 20-26, 2012; arXiv: 1210.5490 [hep-th].
• J. Ben Geloun and Cecilia Flori, Topos Analogues of the KMS State,'' arXiv: 1207.0227 [math-ph].
• I. Aremua, J. Ben Geloun, M. N. Hounkonnou, Deepening the vector coherent state analysis: Revisiting the harmonic oscillator,'' arXiv: 1109.4328 [math-ph].

## Seminars

• Enhanced Quantization on the Circle, The XXIX International Colloquium on Group-Theoretical Methods in Physics, Nankai University, Tianjin, China
• 4D Tensor Field Theory: Asymptotic Freedom, The XXIX International Colloquium on Group-Theoretical Methods in Physics, Nankai University, Tianjin, China
• Renormalizable Tensor Field Theories, Quantum Gravity in Paris, Paris, France
• Quantum Gravity: A short survey, AIMS-Senegal, Mbour, Senegal
• PIRSA:12010132, Tensor Field Theory: Renormalization and One-loop Beta Functions, 2012-01-12, Quantum Gravity
• PIRSA:09120029, Colored group field theory: Scaling properties and positivity, 2009-12-10, Quantum Gravity