Effective action from the functional renormalization group

Abstract

We study the quantum gravitational system coupled to a charged scalar, Dirac fermions, and electromagnetic fields. We use the “exact” or “functional” renormalization group equation to derive the effective action $$\Gamma _0$$ Γ 0 by integrating the flow equation from the ultraviolet scale down to $$k=0$$ k = 0 . The resulting effective action consists of local terms and nonlocal terms with unique coefficients.

Graviton-mediated scattering amplitudes from the quantum effective action

“…1) The form factor formulation naturally includes the one-loop effective action arising from the effective field theory framework of general relativity [16,17], including the universal logarithmic correction terms [48,49,64]. These form factors capture the universal IR behaviour, valid at energy scales well below the UV-cutoff scale.…”

“…The inclusion of higher-order curvature terms in (2.6) is straightforwardly achieved by using irreducible representations of the involved tensor structures. Indeed, recasting the matter interactions found in the oneloop effective field theory [48,49] into the form-factor parameterisation underlying this work gives rise to non-minimal couplings of order R 2 and higher arising from commutators of covariant derivatives. However, these terms only contribute to processes that contain external gravitons or more than four external scalar legs.…”

“…In this approach one takes the viewpoint that a quantum theory is valid up to a UV cutoff scale Λ UV . Starting with a bare action S, one may then compute the cross section by including perturbative (one-loop) corrections to the tree-level Feynman diagrams [16,17,49,[61][62][63][64], also see [18] for a pedagogical introduction. These corrections comprise non-analytic contributions proportional to log s and s −1/2 [16,17].…”

“…For pure gravity one has c 1 = 1/4 and c 2 = 7/20 [48,65] while the Einstein-Hilbert action supplemented by N s minimally coupled, massless scalar fields yields c 1 = 1/4 + N s /72 and c 2 = 7/20 + N s /120. Matter form factors have been given in [49,64].…”

Asymptotic Safety: Swampland or Wonderland?

“…While in this work we have focused on the local sector of the effective action, our computation also yields the coefficients of non-local logarithmic form factors, akin to those arising from non-local heat kernel computations [154][155][156][157][158][159]. It would be interesting to explore their consequences and their role within asymptotically safe gravity [133][134][135] and their connection to massive matter fields [160].…”