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Renormalizable Group Field Theory beyond melonic diagrams: an example in rank four
- Source :
- Physical Review D, Physical Review D, American Physical Society, 2017, 96 (6), pp.066007. ⟨10.1103/PhysRevD.96.066007⟩, Phys.Rev.D, Phys.Rev.D, 2017, 96 (6), pp.066007. ⟨10.1103/PhysRevD.96.066007⟩, Phys.Rev.D, 2017, 96 (6), pp.066007. 〈10.1103/PhysRevD.96.066007〉
- Publication Year :
- 2017
- Publisher :
- HAL CCSD, 2017.
-
Abstract
- We prove the renormalizability of a gauge-invariant, four-dimensional GFT model on SU(2), whose defining interactions correspond to necklace bubbles (found also in the context of new large-N expansions of tensor models), rather than melonic ones, which are not renormalizable in this case. The respective scaling of different interactions in the vicinity of the Gaussian fixed point is determined by the renormalization group itself. This is possible because the appropriate notion of canonical dimension of the GFT coupling constants takes into account the detailed combinatorial structure of the individual interaction terms. This is one more instance of the peculiarity (and greater mathematical richness) of GFTs with respect to ordinary local quantum field theories. We also explore the renormalization group flow of the model at the non-perturbative level, using functional renormalization group methods, and identify a non-trivial fixed point in various truncations. This model is expected to have a similar structure of divergences as the GFT models of 4d quantum gravity, thus paving the way to more detailed investigations on them.<br />30 pages, 15 figures, 2 tables; v2: acknowledgements added; v3: minor modifications (including in the title), matches published version
- Subjects :
- High Energy Physics - Theory
FOS: Physical sciences
Gaussian fixed point
General Relativity and Quantum Cosmology (gr-qc)
Fixed point
renormalizable
01 natural sciences
General Relativity and Quantum Cosmology
[ PHYS.GRQC ] Physics [physics]/General Relativity and Quantum Cosmology [gr-qc]
[ PHYS.HTHE ] Physics [physics]/High Energy Physics - Theory [hep-th]
Theoretical physics
0103 physical sciences
Functional renormalization group
Quantum field theory
010306 general physics
Special unitary group
Physics
010308 nuclear & particles physics
[PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th]
bubble
Renormalization group
High Energy Physics - Theory (hep-th)
SU(2)
Group field theory
[PHYS.GRQC]Physics [physics]/General Relativity and Quantum Cosmology [gr-qc]
Quantum gravity
expansion 1/N
field theory: group
Subjects
Details
- Language :
- English
- ISSN :
- 15507998 and 15502368
- Database :
- OpenAIRE
- Journal :
- Physical Review D, Physical Review D, American Physical Society, 2017, 96 (6), pp.066007. ⟨10.1103/PhysRevD.96.066007⟩, Phys.Rev.D, Phys.Rev.D, 2017, 96 (6), pp.066007. ⟨10.1103/PhysRevD.96.066007⟩, Phys.Rev.D, 2017, 96 (6), pp.066007. 〈10.1103/PhysRevD.96.066007〉
- Accession number :
- edsair.doi.dedup.....f158679b2074a3d87421122678364195