Spectral action approach to higher derivative gravity

Abstract

We study the spectral action approach to higher derivative gravity. The work focuses on the classical aspects. We derive the complete and simplified form of the purely gravitational action up to the 6-derivative terms. We also derive the equivalent forms of the action, which might prove useful in different applications, namely Riemann-and Weyl-dominated representations. The spectral action provides a rather rigid structure of the higher derivative part of the theory. We discuss the possible consequences of this rigidness. As one of the applications, we check whether the conformal backgrounds are preferred in some way on the classical level, with the conclusion that at this level, there is no obvious reason for such a preference, the space S 1 × S 3 studied in earlier works being a special case. Some other possible properties of the higher derivative gravity given by the spectral action are briefly discussed.1 The presence of this function χ(p) and the scale Λ is the reason why the spectral triple almost fixes the spectral action. As we will discuss, they should be considered as independent inputs of the theory, presumably fixed by some fundamental theory of QG.2 Another nice feature of the spectral action is that Higgs field finds its natural place on the geometry side of the picture (rather than on the matter side which is completely encoded in the Hilbert space H). 3 The cut-off function is a non-local object so, strictly speaking it introduces the infinite number of parameters, but in a very controlled way, see below.

Black hole thermodynamics in the presence of nonlinear electromagnetic fields

“…Extensions of the first law for gravitational theories beyond the canonical general relativity, as long as the electromagnetic field is minimally coupled to gravitation, are in principle covered by the covariant phase space formalism procedures [15,69,110,120], although a concrete evaluation of the corrections may be a formidable task. Nontrivial contributions to the gravitational Einstein-Hilbert action can appear, for instance, due to quantization (in a sense of an effective theory) [25,28,39] or quantum gravity (via spectral triple) [29,87]. One line of the future developments are generalizations for the lower and higher dimensional spacetimes, with caveat that invariant G has to be excluded or replaced with something else, as F and its Hodge dual ⋆F have equal orders only in four spacetime dimensions.…”

Introduction to Quantization of Conformal Gravity

“…. ., C 3 1 , and C 3 2 , out of 10 possible terms in the action with six dimension operators [98,99]. There, we also expect that the conformal anomaly A c is described in a conformally covariant way such that A c = b 6 and that only three terms, C C + .…”

Introduction to Quantization of Conformal Gravity

“…. ., C 3 1 , and C 3 2 , out of 10 possible terms in the action with six dimension operators [98,99]. There, we also expect that the conformal anomaly A c is described in a conformally covariant way such that A c = b 6 and that only three terms, C C + .…”