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

A bstract 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 issu...

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Bibliographic Details
Published in:The journal of high energy physics 2020-12, Vol.2020 (12), p.1-54, Article 159
Main Authors: Pithis, Andreas G. A., Thürigen, Johannes
Format: Article
Language:English
Subjects:
Classical and Quantum Gravitation
Elementary Particles
Equivalence
Field theory
Flow equations
Global Symmetries
High energy physics
Mathematical analysis
Models of Quantum Gravity
Nonperturbative Effects
Phase diagrams
Phase transitions
Physics
Physics and Astronomy
Quantum Field Theories
Quantum Field Theory
Quantum gravity
Quantum Physics
Regular Article - Theoretical Physics
Relativity Theory
Renormalization Group
String Theory
Tensors
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Summary:A bstract 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.
ISSN:1029-8479
1029-8479
DOI:10.1007/JHEP12(2020)159