Renormalization of supersymmetric Lifshitz sigma models
Abstract
We study the renormalization of an N = 1 supersymmetric Lifshitz sigma model in three dimensions. The sigma model exhibits worldvolume anisotropy in space and time around the high-energy z = 2 Lifshitz point, such that the worldvolume is endowed with a foliation structure along a preferred time direction. In curved backgrounds, the target-space geometry is equipped with two distinct metrics, and the interacting sigma model is power-counting renormalizable. At low energies, the theory naturally flows toward the relativistic sigma model where Lorentz symmetry emerges. In the superspace formalism, we develop a heat kernel method that is covariantized with respect to the bimetric target-space geometry, using which we evaluate the one-loop beta-functions of the Lifshitz sigma model. This study forms an essential step toward a thorough understanding of the quantum critical supermembrane as a candidate high-energy completion of the relativistic supermembrane.
- Publication:
-
Journal of High Energy Physics
- Pub Date:
- March 2023
- DOI:
- 10.1007/JHEP03(2023)008
- arXiv:
- arXiv:2210.04950
- Bibcode:
- 2023JHEP...03..008Y
- Keywords:
-
- Renormalization Group;
- Sigma Models;
- Superspaces;
- P-Branes;
- High Energy Physics - Theory;
- General Relativity and Quantum Cosmology
- E-Print:
- 35 pages