Abstract
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.
Publisher
Springer Science and Business Media LLC
Subject
Nuclear and High Energy Physics
Reference114 articles.
1. R.M. Williams, Quantum Regge calculus, in Approaches to quantum gravity: toward a new understanding of space, time and matter, D. Oriti ed., Cambridge University Press, Camrbidge U.K. (2009).
2. J. Ambjørn, A. Görlich, J. Jurkiewicz and R. Loll, Nonperturbative quantum gravity, Phys. Rept. 519 (2012) 127 [arXiv:1203.3591] [INSPIRE].
3. R. Gurau, Random tensors, Oxford University Press, Cambridge U.K. (2016).
4. C. Rovelli, Zakopane lectures on loop gravity, PoS(QGQGS2011)003 [arXiv:1102.3660] [INSPIRE].
5. A. Perez, The spin foam approach to quantum gravity, Living Rev. Rel. 16 (2013) 3 [arXiv:1205.2019] [INSPIRE].
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