Fetching the paper…

Reading the bibliography…

2015

Constructive Tensorial Group Field Theory II: The $U(1)-T^4_4$ Model

Lahoche, Vincent

Original
PDF
Post on X

Understand

In this paper we continue our program of non-pertubative constructions of tensorial group field theories (TGFT).

We prove analyticity and Borel summability in a suitable domain of the coupling constant of the simplest super-renormalizable TGFT which contains some ultraviolet divergencies, namely the color-symmetric quartic melonic rank-four model with Abelian $U(1)$ gauge invariance, nicknamed $U(1)-T^4_4$.
We use a multiscale loop vertex expansion.
It is an extension of the loop vertex expansion (the basic constructive technique for non-local theories) which is required for theories that involve non-trivial renormalization.

Constructive Tensorial Group Field Theory II: The $U(1)-T^4_4$ Model · Around

Built on

V. Rivasseau, "From perturbative to constructive renormalization", Princeton University Press (1991)
1991
Earlier work this paper cites.
J. Ambjorn, B. Durhuus and T. Jonsson, “Three-Dimensional Simplicial Quantum Gravity And Generalized Matrix Models,” Mod. Phys. Lett. A 6
1992
Earlier work this paper cites.
C. Rovelli, “The Basis of the Ponzano-Regge-Turaev-Viro-Ooguri quantum gravity model in the loop representation basis,” Phys. Rev. D 48
1993
Earlier work this paper cites.
P. Di Francesco, P. H. Ginsparg and J. Zinn-Justin, “2-D Gravity and random matrices,” Phys. Rept. 254
1995
Earlier work this paper cites.
A. Abdesselam and V. Rivasseau, “Trees, forests and jungles: A Botanical garden for cluster expansions,” Springer Lect. Notes Phys. 446
1995
Earlier work this paper cites.
A. Abdesselam and V. Rivasseau, Lett. Math. Phys. 44
1998
Earlier work this paper cites.
V. Rivasseau, “Constructive Matrix Theory,” JHEP 0709
Original
2010
Earlier work this paper cites.
D. Oriti, “The microscopic dynamics of quantum space as a group field theory,” in Foundations of space and time
Original
2011
Earlier work this paper cites.
R. Gurau, “The 1/N expansion of colored tensor models,” Annales Henri Poincare 12
Original
2011
Earlier work this paper cites.
R. Gurau and V. Rivasseau, “The 1/N expansion of colored tensor models in arbitrary dimension,” Europhys. Lett. 95
Original
2011
Earlier work this paper cites.

Similar

V. Bonzom, R. Gurau, A. Riello and V. Rivasseau, “Critical behavior of colored tensor models in the large N limit,” Nucl. Phys. B 853
Original
2011
Cited alongside, same era.
L. Freidel, R. Gurau and D. Oriti, “Group field theory renormalization - the 3d case: Power counting of divergences,” Phys. Rev. D 80
Original
2011
Cited alongside, same era.
R. Gurau, “The complete 1/N expansion of colored tensor models in arbitrary dimension,” Annales Henri Poincare 13
Original
2012
Cited alongside, same era.
V. Bonzom, R. Gurau, and V. Rivasseau, “Random tensor models in the large N limit: Uncoloring the colored tensor models,” Phys. Rev. D85
Original
2012
Cited alongside, same era.
M. Reuter and F. Saueressig, “Quantum Einstein Gravity,” New J. Phys. 14

Then

S. Carrozza, D. Oriti and V. Rivasseau, “Renormalization of Tensorial Group Field Theories: Abelian U(1) Models in Four Dimensions,” Commun. Math. Phys. 327
Original
2014
Later among the works it cites.
A. Eichhorn and T. Koslowski, “Continuum limit in matrix models for quantum gravity from the Functional Renormalization Group,” Phys. Rev. D 88
Original
2014
Later among the works it cites.
V. Rivasseau and Z. Wang, “How to Resum Feynman Graphs,” Annales Henri Poincare 15
Original
2014
Later among the works it cites.
R. Gurau, "The 1 / N 1/N Expansion of Tensor Models Beyond Perturbation Theory", Comm. Math. Phys.330, 973-1019 (2014), arXiv:1304.2666. T. Delepouve, R. Gurau and V. Rivasseau, "Universality and Borel Summability of Arbitrary Quartic Tensor Models", arXiv:1403.0170 [hep-th]
Original
2014
Later among the works it cites.

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

Original

2012

Cited alongside, same era.

Dine Ousmane Samary, “Beta functions of U(1)d gauge invariant just renormalizable tensor models", Phys.Rev. D88, 105003 (2013) [arXiv:1303.7256[hep-th]]

2013

Cited alongside, same era.

R. Gurau and J. P. Ryan, “Melons are branched polymers,” Annales Henri Poincare 15

2014

Cited alongside, same era.

V. Rivasseau, “Quantum Gravity and Renormalization: The Tensor Track,” AIP Conf. Proc. 1444

2014

Cited alongside, same era.

J. Ben Geloun and V. Rivasseau, “A Renormalizable 4-Dimensional Tensor Field Theory,” Commun. Math. Phys. 318

2014

Cited alongside, same era.

S. Carrozza, D. Oriti and V. Rivasseau, “Renormalization of Tensorial Group Field Theories: Abelian U(1) Models in Four Dimensions,” Commun. Math. Phys. 327

2014

Cited alongside, same era.

V. Lahoche, Constructive Tensorial Group Field Theory I: The U ⁡ ( 1 ) U(1) - T 3 4 T^{4}_{3} Model, arXiv…

Cited in the paper.

D. Benedetti and R. Gurau, “Symmetry breaking in tensor models,” arXiv:1506.08542 [hep-th]

Cited in the paper.

D. Oriti, “Group field theory as the 2nd quantization of Loop Quantum Gravity,” arXiv:1310.7786 [gr-qc]; D. Oriti, “Group Field Theory and Loop Quantum Gravity,” arXiv:1408.7112 [gr-qc]; D. Oriti, J. P. Ryan and J. Thürigen, “Group field theories for all loop quantum gravity,” New J.Phys. 17, 023042 (2015) [arXiv:1409.3150 [gr-qc]]

2015

Closest in time.

T. Delepouve and R. Gurau, “Phase Transition in Tensor Models,” JHEP 1506

2015

Closest in time.

V. Lahoche, D. Oriti and V. Rivasseau, “Renormalization of an Abelian Tensor Group Field Theory: Solution at Leading Order,” JHEP 1504

2015

Closest in time.

D. Benedetti, J. Ben Geloun and D. Oriti, “Functional Renormalisation Group Approach for Tensorial Group Field Theory: a Rank-3 Model,” JHEP 1503

2015

Closest in time.

S. Carrozza, “Group field theory in dimension 4 − ϵ 4-\epsilon ,” Phys. Rev. D 91

2015

Closest in time.

D. O. Samary and F. Vignes-Tourneret, “Just Renormalizable TGFT’s on U ( 1 ) d U(1)^{d} with Gauge Invariance,” Commun. Math. Phys. 329

2096

Closest in time.