scholarly journals Functional renormalization group for theU(1)−T56tensorial group field theory with closure constraint

2017 ◽  
Vol 95 (4) ◽  
Author(s):  
Vincent Lahoche ◽  
Dine Ousmane Samary
Keyword(s):  
Field Theory ◽  
Renormalization Group ◽  
Functional Renormalization Group ◽  
Group Field Theory ◽  
Closure Constraint

scholarly journals Functional renormalization group analysis of rank-3 tensorial group field theory: The full quartic invariant truncation

2018 ◽  
Vol 97 (12) ◽  
Author(s):  
Joseph Ben Geloun ◽  
Tim A. Koslowski ◽  
Daniele Oriti ◽  
Antonio D. Pereira
Keyword(s):  
Field Theory ◽  
Renormalization Group ◽  
Group Analysis ◽  
Renormalization Group Analysis ◽  
Functional Renormalization Group ◽  
Group Field Theory

scholarly journals Phase transitions in TGFT: functional renormalization group in the cyclic-melonic potential approximation and equivalence to O(N) models

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Andreas G. A. Pithis ◽  
Johannes Thürigen
Keyword(s):  
Field Theory ◽  
Renormalization Group ◽  
Fixed Points ◽  
Group Method ◽  
Constant Field ◽  
Theory Approach ◽  
Specific Flow ◽  
Functional Renormalization Group ◽  
Spacetime Geometry ◽  
Group Field Theory

Abstract In the group field theory approach to quantum gravity, continuous spacetime geometry is expected to emerge via phase transition. However, understanding the phase diagram and finding fixed points under the renormalization group flow remains a major challenge. In this work we tackle the issue for a tensorial group field theory using the functional renormalization group method. We derive the flow equation for the effective potential at any order restricting to a subclass of tensorial interactions called cyclic melonic and projecting to a constant field in group space. For a tensor field of rank r on U(1) we explicitly calculate beta functions and find equivalence with those of O(N) models but with an effective dimension flowing from r − 1 to zero. In the r − 1 dimensional regime, the equivalence to O(N) models is modified by a tensor specific flow of the anomalous dimension with the consequence that the Wilson-Fisher type fixed point solution has two branches. However, due to the flow to dimension zero, fixed points describing a transition between a broken and unbroken phase do not persist and we find universal symmetry restoration. To overcome this limitation, it is necessary to go beyond compact configuration space.

scholarly journals Functional Renormalization Group analysis of a Tensorial Group Field Theory on $\mathbb{R}^3$

2015 ◽  
Vol 112 (3) ◽  
pp. 31001 ◽  
Author(s):  
Joseph Ben Geloun ◽  
Riccardo Martini ◽  
Daniele Oriti
Keyword(s):  
Field Theory ◽  
Renormalization Group ◽  
Group Analysis ◽  
Renormalization Group Analysis ◽  
Functional Renormalization Group ◽  
Group Field Theory

scholarly journals Progress in Solving the Nonperturbative Renormalization Group for Tensorial Group Field Theory

Universe ◽  
2019 ◽  
Vol 5 (3) ◽  
pp. 86 ◽  
Author(s):  
Vincent Lahoche ◽  
Dine Ousmane Samary
Keyword(s):  
Field Theory ◽  
Renormalization Group ◽  
Fixed Points ◽  
Expansion Method ◽  
Flow Equation ◽  
Nucl Phys ◽  
Flow Equations ◽  
First Order Phase Transition ◽  
Group Field Theory ◽  
Non Gaussian

This manuscript aims at giving new advances on the functional renormalization group applied to the tensorial group field theory. It is based on the series of our three papers (Lahoche, et al., Class. Quantum Gravity 2018, 35, 19), (Lahoche, et al., Phys. Rev. D 2018, 98, 126010) and (Lahoche, et al., Nucl. Phys. B, 2019, 940, 190–213). We consider the polynomial Abelian U ( 1 ) d models without the closure constraint. More specifically, we discuss the case of the quartic melonic interaction. We present a new approach, namely the effective vertex expansion method, to solve the exact Wetterich flow equation and investigate the resulting flow equations, especially regarding the existence of non-Gaussian fixed points for their connection with phase transitions. To complete this method, we consider a non-trivial constraint arising from the Ward–Takahashi identities and discuss the disappearance of the global non-trivial fixed points taking into account this constraint. Finally, we argue in favor of an alternative scenario involving a first order phase transition into the reduced phase space given by the Ward constraint.

scholarly journals Discrete renormalization group for SU(2) tensorial group field theory

2015 ◽  
Vol 2 (1) ◽  
pp. 49-112 ◽  
Author(s):  
Sylvain Carrozza
Keyword(s):  
Field Theory ◽  
Renormalization Group ◽  
Group Field Theory
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