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

Vincent Lahoche; Daniele Oriti

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arXiv · 1506.08393

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

Vincent Lahoche·Daniele Oriti

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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.

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Vincent Lahoche, Daniele Oriti. 2015-06-28. Renormalization of a tensorial field theory on the homogeneous space SU(2)/U(1). https://arxiv.org/abs/1506.08393

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