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Register a new userGauge Dependence of the Effective Average Action in Einstein Gravity
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Authors
S. Falkenberg
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We study the gauge dependence of the effective average action Gamma_k and Newtonian gravitational constant using the RG equation for Gamma_k. Then we truncate the space of action functionals to get a solution of this equation. We solve the truncated evolution equation for the Einstein gravity in the De Sitter background for a general gauge parameter alpha and obtain a system of equations for the cosmological and the Newtonian constants. Analyzing the running of the gravitational constant we find that the Newtonian constant depends strongly on the gauge parameter. This leads to the appearance of antiscreening and screening behavior of the quantum gravity. The resolution of the gauge dependence problem is suggested. For physical gauges like the Landau-De Witt gauge the Newtonian constant shows an antiscreening.
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The gauge dependence of effective average action in the functional renormalization group is studied. The effective average action is considered as non-perturbative solution to the flow equation which is the basic equation of the method. It is proven that at any scale of IR cutoff the effective average action depends on gauges making impossible physical interpretation of all obtained results in this method.
Using the background field method for the functional renormalization group approach in the case of a generic gauge theory, we study the background field symmetry and gauge dependence of the background average effective action, when the regulator action depends on external fields. The final result is that the symmetry of the average effective action can be maintained for a wide class of regulator functions, but in all cases the dependence of the gauge fixing remains on-shell. The Yang-Mills theory is considered as the main particular example.
The divergent part of the one-loop Vilkovisky unique effective action for quantum Einstein gravity is evaluated in the general parametrization of the quantum field, including the separated conformal factor. The output of this calculation explicitly demonstrates the parametrization and conformal gauge independence of the unique effective action with the configuration space metric chosen following Vilkoviskys prescription.
We explicitly demonstrate that the perturbative holomorphic contribution to the off-shell effective action of N=2 U(1) gauge supermultiplet is an entire effect of the minimal coupling to a hypermultiplet with the mass generated by a central charge in N=2 superalgebra. The central charge is induced by a constant vacuum N=2 gauge superfield strength spontaneously breaking the automorphism U(1)_R symmetry of N=2 superalgebra. We use the manifestly off-shell supersymmetric harmonic superspace techniques of quantum calculations with the central charge-massive hypermultiplet propagator.
We investigate the gauge symmetry and gauge fixing dependence properties of the effective average action for quantum gravity models of general form. Using the background field formalism and the standard BRST-based arguments, one can establish the special class of regulator functions that preserves the background field symmetry of the effective average action. Unfortunately, regardless the gauge symmetry is preserved at the quantum level, the non-invariance of the regulator action under the global BRST transformations leads to the gauge fixing dependence even under the use of the on-shell conditions.
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