Emergence of spacetime in a restricted spin-foam model

Thürigen

2020

J. High Energ. Phys.

Self Cite

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.

Section: Conclusion and Discussionmentioning

confidence: 99%

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

Thürigen

2020

J. High Energ. Phys.

Self Cite

“…Similarly, RG techniques are being developed and applied in the search for a critical point in spin foams, see [72,73]. In this setting, studies of the phase diagram of quantum gravity have only recently started [74][75][76][77]. In contrast, in the Euclidean and Causal Dynamical Triangulation approaches (EDT, CDT) [11,12,78,79], much is already known about the phase diagram.…”

Section: Jhep12(2020)131mentioning

confidence: 99%

The phase diagram of the multi-matrix model with ABAB interaction from functional renormalization

Eichhorn

Pereira

2020

J. High Energ. Phys.

At criticality, discrete quantum-gravity models are expected to give rise to continuum spacetime. Recent progress has established the functional renormalization group method in the context of such models as a practical tool to study their critical properties and to chart their phase diagrams. Here, we apply these techniques to the multi-matrix model with ABAB interaction potentially relevant for Lorentzian quantum gravity in 3 dimensions. We characterize the fixed-point structure and phase diagram of this model, paving the way for functional RG studies of more general multi-matrix or tensor models encoding causality and subjecting the technique to another strong test of its performance in discrete quantum gravity by comparing to known results.

“…From the physical perspective of the discrete geometries, another possibility is that such a phase transition should be characterized by arbitrary large fluctuations in GFT momentum space given by group representations since these are the eigenmodes of length, area or volume operators of such geometries [32]. While this has been explored in spin foam models [33], the usual GFT propagator does not allow for such a notion of correlation length.…”

Section: Phase Transition In Group Field Theorymentioning

confidence: 99%

Phase transitions in group field theory: The Landau perspective

Thürigen

2018

Phys. Rev. D

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In various approaches to quantum gravity continuum spacetime is expected to emerge from discrete geometries through a phase transition. In group field theory, various indications for such a transition have recently been found but a complete understanding of such a phenomenon remains an open issue. In this work, we investigate the critical behavior of different group field theory models in the Gaussian approximation. Applying the Ginzburg criterion to quantify field fluctuations, we find that this approximation breaks down in the case of three-dimensional Euclidean quantum gravity as described by the dynamical Boulatov model on the compact group SU(2). This result is independent of the peculiar gauge symmetry and specific form of nonlocality of the model. On the contrary, we find that the Gaussian approximation is valid for a rank-1 GFT on the noncompact sector of fields on SL(2, R) related to Lorentzian models. Though a nonperturbative analysis is needed to settle the question of phase transitions for compact groups, the results may also indicate the necessity to consider group field theory on noncompact domains for phase transitions to occur.