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Renormalization of an SU(2) Tensorial Group Field Theory in Three Dimensions

MPG-Autoren
http://pubman.mpdl.mpg.de/cone/persons/resource/persons41482

Carrozza,  Sylvain
Microscopic Quantum Structure & Dynamics of Spacetime, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons20698

Oriti,  Daniele
Microscopic Quantum Structure & Dynamics of Spacetime, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Volltexte (frei zugänglich)

1303.6772
(Preprint), 561KB

CMP330_581.pdf
(beliebiger Volltext), 943KB

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Zitation

Carrozza, S., Oriti, D., & Rivasseau, V. (2014). Renormalization of an SU(2) Tensorial Group Field Theory in Three Dimensions. Communications in Mathematical Physics, 330(2), 581-637. doi:10.1007/s00220-014-1928-x.


Zitierlink: http://hdl.handle.net/11858/00-001M-0000-000E-EC5C-2
Zusammenfassung
We address in this paper the issue of renormalizability for SU(2) Tensorial Group Field Theories (TGFT) with geometric Boulatov-type conditions in three dimensions. We prove that tensorial interactions up to degree 6 are just renormalizable without any anomaly. Our new models define the renormalizable TGFT version of the Boulatov model and provide therefore a new approach to quantum gravity in three dimensions. Among the many new technical results established in this paper are a general classification of just renormalizable models with gauge invariance condition, and in particular concerning properties of melonic graphs, the second order expansion of melonic two point subgraphs needed for wave-function renormalization.