Abstract
We develop a new heat kernel method that is suited for a systematic study of the renormalization group flow in Hořava 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.
Highlights
Despite the desirable features of Hořava gravity, it still faces the challenge of explaining the vast catalogue of experimental data that highly constrains Lorentz violation [4]
We develop a new heat kernel method that is suited for a systematic study of the renormalization group flow in Hořava gravity
Regardless of whether or not Hořava gravity is phenomenologically viable for describing our universe in 3 + 1 dimensions, it still has a plethora of important applications in the context of the AdS/CFT correspondence for nonrelativistic systems [10,11,12,13,14], the Causal Dynamical Triangulation approach to quantum gravity [15, 16], the formulation of membranes at quantum criticality [2], the geometric theory of Ricci flow on Riemannian manifolds [17], and so on
Summary
Consider a QFT on a d-dimensional Riemannian manifold M equipped with a metric gμν for a field configuration ΦA(x), where xμ, μ = 0, · · · , d − 1 denotes a set of coordinates on M.4. The field ΦA can have a general tensor structure and A denotes collectively its indices. We assume that the QFT is described by an action principle S[Φ], which expands as. We have introduced the heat kernel for the operator O in (2.8), KO(x, x0 | τ ) = x|e−τ O|x0 ,. Note that the symbol KO without arguments and the name “heat kernel” will be used interchangeably to refer to the operator e−τ O in general or to the specific coordinate space representation of this operator, KO(x, x0 | τ )
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