Quantum gravity, effective fields and string theory

TL;DR

This paper explores quantum gravity as an effective field theory, calculating quantum corrections to classical metrics, examining string theory relations, and analyzing the behavior of gravity in infinite dimensions.

Contribution

It provides new calculations of quantum corrections to gravitational metrics and extends string theory relations to effective operators, offering insights into quantum gravity's structure.

Findings

Quantum corrections to Schwarzschild and Kerr metrics calculated.

String theory relations extended to effective field theories.

Planar graphs dominate in the infinite-dimensional limit.

Abstract

We look at the various aspects of treating general relativity as a quantum theory. It is briefly studied how to consistently quantize general relativity as an effective field theory. A key achievement here is the long-range low-energy leading quantum corrections to both the Schwarzschild and Kerr metrics. The leading quantum corrections to the pure gravitational potential between two sources are also calculated, both in the mixed theory of scalar QED and quantum gravity and in the pure gravitational theory. The (Kawai-Lewellen-Tye) string theory gauge/gravity relations is next dealt with. We investigate if the KLT-operator mapping extends to the case of higher derivative effective operators. The KLT-relations are generalized, taking the effective field theory viewpoint, and remarkable tree-level amplitude relations between the field theory operators are derived. Quantum gravity is finally looked at from the the perspective of taking the limit of infinitely many spatial dimensions. It is verified that only a certain class of planar graphs will in fact contribute to the $n$-point functions at $D=\infty$. This limit is somewhat an analogy to the large-N limit of gauge theories although the interpretation of such a graph limit in a gravitational framework is quite different.