Quantum Topological Invariants, Gravitational Instantons and the Topological Embedding

TL;DR

This paper explores topological invariants of gravitational instantons, introduces a topological embedding framework for physical amplitudes, and applies it to compute correlation functions and quantum effects in punctured gravitational backgrounds.

Contribution

It defines new topological invariants, introduces the concept of punctures in four-dimensional instantons, and develops a topological embedding method for calculating quantum amplitudes.

Findings

Computed amplitudes in 2D and 4D topological gravity.

Introduced the notion of puncture in four-dimensional instantons.

Applied topological embedding to Dirac fermions, QED, and QCD amplitudes.

Abstract

Certain topological invariants of the moduli space of gravitational instantons are defined and studied. Several amplitudes of two and four dimensional topological gravity are computed. A notion of puncture in four dimensions, that is particularly meaningful in the class of Weyl instantons, is introduced. The topological embedding, a theoretical framework for constructing physical amplitudes that are well-defined order by order in perturbation theory around instantons, is explicitly applied to the computation of the correlation functions of Dirac fermions in a punctured gravitational background, as well as to the most general QED and QCD amplitude. Various alternatives are worked out, discussed and compared. The quantum background affects the propagation by generating a certain effective ``quantum'' metric. The topological embedding could represent a new chapter of quantum field theory.