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New heat kernel method in Lifshitz theories. (English) Zbl 1462.83041

Summary: 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.

MSC:

83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field theories
83C45 Quantization of the gravitational field
81T17 Renormalization group methods applied to problems in quantum field theory
35K08 Heat kernel

Software:

xAct
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

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