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Quantizing nonprojectable Hořava gravity with Lagrangian path integral

D. Blas1,2, F. Del Porro3,4,*, M. Herrero-Valea5, J. Radkovski6,7,†, and S. Sibiryakov6,7

  • *Contact author: francesco.del.porro@nbi.ku.dk
  • †Contact author: jradkovski@perimeterinstitute.ca
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Phys. Rev. D 113, 106022 – Published 19 May, 2026

DOI: https://doi.org/10.1103/ptvr-yb3y

Abstract

We formulate the q uantum version of nonprojectable Hořava gravity as a Lagrangian theory with a path integral in the configuration space with an ultralocal in time, but nonlocal in space, field-dependent measure. Using auxiliary fields, we cast the measure into a local form satisfying several bosonic and fermionic symmetries. We perform an explicit one-loop computation in the theory in (2+1) dimensions, using for the case study the divergent part of the action on a background with nontrivial shift vector; the background spatial metric is taken to be flat and the background lapse function is set to 1. No truncations are assumed at the level of perturbations, for which we develop a diagrammatic technique and a version of the heat-kernel method. We isolate dangerous linear-in-frequency divergences in the two-point function of the shift, which can lead to spatial nonlocalities, and explicitly verify their cancellation. This leaves a fully local expression for the divergent part of the quadratic effective action, from which we extract the beta functions for the Newton constant and the essential coupling λ in the kinetic term of the metric. We formulate the questions that need to be addressed to prove perturbative renormalizability of the nonprojectable Hořava gravity.

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Phys. Rev. D 113, 106022– Published 19 May, 2026
  • Received 16 January 2026
  • Accepted 23 March 2026
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