Canonical differential geometry of string backgrounds

TL;DR

This paper explores the geometry of string backgrounds using area metric geometry, extending traditional metric concepts to better describe D-branes and their gravitational dynamics.

Contribution

It introduces the differential geometric structure relevant for minimal surface equations in area metric geometry, generalizing classical metric geometry.

Findings

Identifies the appropriate differential structure for area metric spaces

Introduces a derivative action of areas on areas

Suggests new tools for gravitational dynamics on D-branes

Abstract

String backgrounds and D-branes do not possess the structure of Lorentzian manifolds, but that of manifolds with area metric. Area metric geometry is a true generalization of metric geometry, which in particular may accommodate a B-field. While an area metric does not determine a connection, we identify the appropriate differential geometric structure which is of relevance for the minimal surface equation in such a generalized geometry. In particular the notion of a derivative action of areas on areas emerges naturally. Area metric geometry provides new tools in differential geometry, which promise to play a role in the description of gravitational dynamics on D-branes.