23 сентября 2022 г.
А.Куров
Модели квантовой гравитации и их анализ методом ренормгруппы
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
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