New Heat Kernel Method in Lifshitz Theories

Abstract

We develop a new heat kernel method that is suited for a systematic study of the renormalization group flow in Horava gravity (and in Lifshitz field theories in general). This method maintains covariance at all stages of the calculation, which is achieved by introducing a generalized Fourier transform covariant with respect to the nonrelativistic background spacetime. As a first test, we apply this method to compute the anisotropic Weyl anomaly for a (2+1)-dimensional scalar field theory around a z=2 Lifshitz point and corroborate the previously found result. We then proceed to general scalar operators and evaluate their one-loop effective action. The covariant heat kernel method that we develop also directly applies to operators with spin structures in arbitrary dimensions.

47 pages, 1 figure; v2: appendix C updated, minor typos corrected, references added; v3: typos fixed

References in corpus (30)

• Quantum Gravity at a Lifshitz Point
• Heat kernel expansion: user's manual
• Spectral Dimension of the Universe in Quantum Gravity at a Lifshitz Point
• Membranes at Quantum Criticality
• General Covariance in Quantum Gravity at a Lifshitz Point
• Torsional Newton-Cartan Geometry and Lifshitz Holography
• Boundary Stress-Energy Tensor and Newton-Cartan Geometry in Lifshitz Holography
• Lorentz Violation in Supersymmetric Field Theories
• Horava-Lifshitz Gravity From Dynamical Newton-Cartan Geometry
• Lifshitz Gravity for Lifshitz Holography
• Renormalization of Horava Gravity
• General Covariance in Gravity at a Lifshitz Point
• Conformal Lifshitz Gravity from Holography
• Hořava gravity is asymptotically free (in 2+1 dimensions)
• Quantum Gravity via Causal Dynamical Triangulations
• Anomalous Breaking of Anisotropic Scaling Symmetry in the Quantum Lifshitz Model
• Gravitational effective action and entanglement entropy in UV modified theories with and without Lorentz symmetry
• Emergent Lorentz invariance from Strong Dynamics: Holographic examples
• Towards the renormalization group flow of Horava gravity in $(3+1)$ dimensions
• One-loop renormalization in a toy model of Horava-Lifshitz gravity
• The emergence of a universal limiting speed
• Lifshitz Scale Anomalies
• Heat kernel methods for Lifshitz theories
• Quantization of Horava Gravity in 2+1 Dimensions
• Closure of the algebra of constraints for a nonprojectable Hořava model
• Heat kernel coefficients on the sphere in any dimension
• Heat Kernel Expansion for Operators of the Type of the Square Root of the Laplace Operator
• Revisiting Lorentz violation in Horava gravity
• Heat kernel for flat generalized Laplacians with anisotropic scaling
• Abelian M5-brane on $S^6$

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• Heat kernel expansion for higher order minimal and nonminimal operators
• Renormalization of Supersymmetric Lifshitz Sigma Models
• Strings in Bimetric Spacetimes