Progress in Solving the Nonperturbative Renormalization Group for Tensorial Group Field Theory
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....
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MDPI AG
2019-03-01
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| Online Access: | https://www.mdpi.com/2218-1997/5/3/86 |
| _version_ | 1797999064297504768 |
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| author | Vincent Lahoche Dine Ousmane Samary |
| author_facet | Vincent Lahoche Dine Ousmane Samary |
| author_sort | Vincent Lahoche |
| collection | DOAJ |
| description | 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 <inline-formula> <math display="inline"> <semantics> <mrow> <mi>U</mi> <msup> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> <mi>d</mi> </msup> </mrow> </semantics> </math> </inline-formula> 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. |
| first_indexed | 2024-04-11T10:58:39Z |
| format | Article |
| id | doaj.art-56737eee362a4afcbd5b3c9ddbf5f7ce |
| institution | Directory Open Access Journal |
| issn | 2218-1997 |
| language | English |
| last_indexed | 2024-04-11T10:58:39Z |
| publishDate | 2019-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Universe |
| spelling | doaj.art-56737eee362a4afcbd5b3c9ddbf5f7ce2022-12-22T04:28:41ZengMDPI AGUniverse2218-19972019-03-01538610.3390/universe5030086universe5030086Progress in Solving the Nonperturbative Renormalization Group for Tensorial Group Field TheoryVincent Lahoche0Dine Ousmane Samary1Commissariat à l’Énergie Atomique (CEA, LIST), 8 Avenue de la Vauve, 91120 Palaiseau, FranceCommissariat à l’Énergie Atomique (CEA, LIST), 8 Avenue de la Vauve, 91120 Palaiseau, FranceThis 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 <inline-formula> <math display="inline"> <semantics> <mrow> <mi>U</mi> <msup> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> <mi>d</mi> </msup> </mrow> </semantics> </math> </inline-formula> 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.https://www.mdpi.com/2218-1997/5/3/86nonperturbative renormalization groupquantum gravityrandom geometry |
| spellingShingle | Vincent Lahoche Dine Ousmane Samary Progress in Solving the Nonperturbative Renormalization Group for Tensorial Group Field Theory Universe nonperturbative renormalization group quantum gravity random geometry |
| title | Progress in Solving the Nonperturbative Renormalization Group for Tensorial Group Field Theory |
| title_full | Progress in Solving the Nonperturbative Renormalization Group for Tensorial Group Field Theory |
| title_fullStr | Progress in Solving the Nonperturbative Renormalization Group for Tensorial Group Field Theory |
| title_full_unstemmed | Progress in Solving the Nonperturbative Renormalization Group for Tensorial Group Field Theory |
| title_short | Progress in Solving the Nonperturbative Renormalization Group for Tensorial Group Field Theory |
| title_sort | progress in solving the nonperturbative renormalization group for tensorial group field theory |
| topic | nonperturbative renormalization group quantum gravity random geometry |
| url | https://www.mdpi.com/2218-1997/5/3/86 |
| work_keys_str_mv | AT vincentlahoche progressinsolvingthenonperturbativerenormalizationgroupfortensorialgroupfieldtheory AT dineousmanesamary progressinsolvingthenonperturbativerenormalizationgroupfortensorialgroupfieldtheory |