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.

35 pages; v2: published version, two references added

References in corpus (9)

• Quantum Gravity at a Lifshitz Point
• Membranes at Quantum Criticality
• Topological Order and Conformal Quantum Critical Points
• Goldstones with Extended Shift Symmetries
• Dual D-Brane Actions in Nonrelativistic String Theory
• Renormalization properties of a Galilean Wess-Zumino model
• Supersymmetric Galilean Electrodynamics
• New Heat Kernel Method in Lifshitz Theories
• Strings in Bimetric Spacetimes

Cited by in corpus (2)

• Aspects of Non-Relativistic Quantum Field Theories
• Worldsheet Formalism for Decoupling Limits in String Theory