Gerbes, Quantum Mechanics and Gravity

TL;DR

This paper establishes a link between duality invariance in quantum theories, noncommutative geometry, and gerbes, providing insights into the structure of quantum gravity and the geometric nature of quantum states.

Contribution

It demonstrates that duality invariance implies noncommutative geometry and connects these concepts to gerbes and B-fields, offering a novel geometric perspective on quantum gravity.

Findings

Duality invariance corresponds to noncommutative space coordinates.

Gerbes and B-fields are related to quantum dualities and gravity.

Feynman's propagator is linked to gerbe trivialisation.

Abstract

We prove that invariance of a quantum theory under the semiclassical vs. strong-quantum duality $S/\hbar\longleftrightarrow\hbar/S$, where S is the classical action, is equivalent to noncommutativity (of the Heisenberg-algebra type) of the coordinates of the space on which S is defined. We place these facts in correspondence with gerbes and Neveu-Schwarz B-fields and discuss their implications for a quantum theory of gravity. Feynman's propagator turns out to be closely related to the trivialisation of a gerbe on configuration space.