Phase transitions in TGFT: functional renormalization group in the cyclic-melonic potential approximation and equivalence to O(N) models
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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2020-12-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP12(2020)159 |
| _version_ | 1818920440732581888 |
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| author | Andreas G. A. Pithis Johannes Thürigen |
| author_facet | Andreas G. A. Pithis Johannes Thürigen |
| author_sort | Andreas G. A. Pithis |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-20T01:21:47Z |
| format | Article |
| id | doaj.art-9104ba81689746febfb688ad413ad861 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-20T01:21:47Z |
| publishDate | 2020-12-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-9104ba81689746febfb688ad413ad8612022-12-21T19:58:25ZengSpringerOpenJournal of High Energy Physics1029-84792020-12-0120201215410.1007/JHEP12(2020)159Phase transitions in TGFT: functional renormalization group in the cyclic-melonic potential approximation and equivalence to O(N) modelsAndreas G. A. Pithis0Johannes Thürigen1Scuola Internazionale Superiore di Studi Avanzati (SISSA)Mathematisches Institut der Westfälischen Wilhelms-Universität MünsterAbstract 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.https://doi.org/10.1007/JHEP12(2020)159Renormalization GroupGlobal SymmetriesNonperturbative EffectsModels of Quantum Gravity |
| spellingShingle | Andreas G. A. Pithis Johannes Thürigen Phase transitions in TGFT: functional renormalization group in the cyclic-melonic potential approximation and equivalence to O(N) models Journal of High Energy Physics Renormalization Group Global Symmetries Nonperturbative Effects Models of Quantum Gravity |
| title | Phase transitions in TGFT: functional renormalization group in the cyclic-melonic potential approximation and equivalence to O(N) models |
| title_full | Phase transitions in TGFT: functional renormalization group in the cyclic-melonic potential approximation and equivalence to O(N) models |
| title_fullStr | Phase transitions in TGFT: functional renormalization group in the cyclic-melonic potential approximation and equivalence to O(N) models |
| title_full_unstemmed | Phase transitions in TGFT: functional renormalization group in the cyclic-melonic potential approximation and equivalence to O(N) models |
| title_short | Phase transitions in TGFT: functional renormalization group in the cyclic-melonic potential approximation and equivalence to O(N) models |
| title_sort | phase transitions in tgft functional renormalization group in the cyclic melonic potential approximation and equivalence to o n models |
| topic | Renormalization Group Global Symmetries Nonperturbative Effects Models of Quantum Gravity |
| url | https://doi.org/10.1007/JHEP12(2020)159 |
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