Speaker
Description
We derive the full set of beta functions for the marginal essential
couplings of projectable Horava gravity in $(3+1)$-dimensional
spacetime. To this end we compute the divergent part of the one-loop
effective action in static background with arbitrary spatial
metric. The computation is done in several steps: reduction of the
problem to three dimensions, extraction of an operator square root from
the spatial part of the fluctuation operator, and evaluation of its
trace using the method of universal functional traces. This provides
us with the renormalization of couplings in the potential part of the
action which we combine with the results for the
kinetic part obtained previously. The calculation uses
symbolic computer algebra and is performed in four different gauges
yielding identical results for the essential beta functions. We
additionally check the calculation by evaluating the effective action
on a special background with spherical spatial slices using an
alternative method of spectral summation. We conclude with a
preliminary discussion of the properties of the beta functions and the
resulting renormalization group flow, identifying several candidate
asymptotically free fixed points.
