Renormalizable acausal theories of classical gravity coupled with interacting quantum fields

Abstract

We prove the renormalizability of various theories of classical gravity coupled with interacting quantum fields. The models contain vertices with dimensionality greater than four, a finite number of matter operators and a finite or reduced number of independent couplings. An interesting class of models is obtained from ordinary power-counting renormalizable theories, letting the couplings depend on the scalar curvature R of spacetime. The divergences are removed without introducing higher-derivative kinetic terms in the gravitational sector. The metric tensor has a non-trivial running, even if it is not quantized. The results are proved applying a certain map that converts classical instabilities, due to higher derivatives, into classical violations of causality, whose effects become observable at sufficiently high energies. We study acausal Einstein-Yang-Mills theory with an R-dependent gauge coupling in detail. We derive all-order formulas for the beta functions of the dimensionality-six gravitational vertices induced by renormalization, such as RR µνρσ R µνρσ . Such beta functions are related to the trace-anomaly coefficients of the matter subsector.

Properties of the classical action of quantum gravity

“…Finally, recall that when maps such as (5.1) and (5.4) lower the number of time derivatives, they also generate violations of microcausality [13,19], to which the arguments of the previous section apply.…”

Neutron Stars on Modified Teleparallel Gravity

“…In TEGR, the equations equivalent to Eqs. ( 9) and (10) are not a set of independent equations. There, a standard procedure consists in manipulating three of the equations and showing that the fourth is obtained.…”

“…Some of the failures of the standard GR (in particular, the accelerated expansion of the Universe and galaxy rotation curves) may be solved by the proposition of the existence of exotic matter (dark matter) and dark energy, both of them composing the so called "dark sector" [1][2][3][4][5][6][7][8]. However, even in the presence of the dark sector, some problems still remain in high-energy regimes, where quantization is expected [9,10].…”

Causality in Nonlocal Gravity

“…The propagator of the theory (38) is very similar to (19), but shows up two complex conjugate poles,…”

“…General causal nonlocal theories -In this section we shortly remind a field redefinition theorem [19,20] that allows us to map nonlocal field theories to local ones at tree-level. The theorem is perturbative in the field redefinition, but the identification is only valid at tree-level because of the different quantum properties of the two theories.…”