QFT with Tensorial and Local Degrees of Freedom: Phase Structure from Functional Renormalization
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866910351663038464 |
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| author | Geloun, Joseph Ben Pithis, Andreas G. A. Thürigen, Johannes |
| author_facet | Geloun, Joseph Ben Pithis, Andreas G. A. Thürigen, Johannes |
| contents | Field theories with combinatorial non-local interactions such as tensor invariants are interesting candidates for describing a phase transition from discrete quantum-gravitational to continuum geometry. In the so-called cyclic-melonic potential approximation of a tensorial field theory on the $r$-dimensional torus it was recently shown using functional renormalization group techniques that no such phase transition to a condensate phase with a tentative continuum geometric interpretation is possible. Here, keeping the same approximation, we show how to overcome this limitation amending the theory by local degrees freedom on $\mathbb{R}^d$. We find that the effective $r-1$ dimensions of the torus part dynamically vanish along the renormalization group flow while the $d$ local dimensions persist up to small momentum scales. Consequently, for $d>2$ one can find a phase structure allowing also for phase transitions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_06136 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | QFT with Tensorial and Local Degrees of Freedom: Phase Structure from Functional Renormalization Geloun, Joseph Ben Pithis, Andreas G. A. Thürigen, Johannes High Energy Physics - Theory General Relativity and Quantum Cosmology Mathematical Physics Field theories with combinatorial non-local interactions such as tensor invariants are interesting candidates for describing a phase transition from discrete quantum-gravitational to continuum geometry. In the so-called cyclic-melonic potential approximation of a tensorial field theory on the $r$-dimensional torus it was recently shown using functional renormalization group techniques that no such phase transition to a condensate phase with a tentative continuum geometric interpretation is possible. Here, keeping the same approximation, we show how to overcome this limitation amending the theory by local degrees freedom on $\mathbb{R}^d$. We find that the effective $r-1$ dimensions of the torus part dynamically vanish along the renormalization group flow while the $d$ local dimensions persist up to small momentum scales. Consequently, for $d>2$ one can find a phase structure allowing also for phase transitions. |
| title | QFT with Tensorial and Local Degrees of Freedom: Phase Structure from Functional Renormalization |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology Mathematical Physics |
| url | https://arxiv.org/abs/2305.06136 |