Renormalization of a tensorial field theory on the homogeneous space SU(2)/U(1)

Lahoche, Vincent; Oriti, Daniele

doi:10.1088/1751-8113/50/2/025201

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Renormalization of a tensorial field theory on the homogeneous space SU(2)/U(1)

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

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Lahoche, V., & Oriti, D. (2017). Renormalization of a tensorial field theory on the homogeneous space SU(2)/U(1). Journal of Physics A, 50(2): 025201. doi:10.1088/1751-8113/50/2/025201.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0028-1E04-8

Abstract

We study the renormalization of a general field theory on the 2-sphere with tensorial interaction and gauge invariance under the diagonal action of SU(2). We derive the power counting for arbitrary dimension d. For the case d=4, we prove perturbative renormalizability to all orders via multi-scale analysis, study both the renormalised and effective perturbation series, and establish the asymptotic freedom of the model. We also outline a general power counting for the homogeneous space SO(D)/SO(D-1), of direct interest for quantum gravity models in general dimensions, and point out the obstructions to the direct generalisation of our results to these cases.