Almost product manifolds as the low energy geometry of Dirichlet branes

TL;DR

This paper explores how low-energy dynamics of curved Dirichlet p-branes in string theory exhibit an almost product structure, encoding minimal length and maximal speed, leading to new kinematic effects relevant for quantum gravity phenomenology.

Contribution

It demonstrates that Dirichlet p-branes possess an extended isometry group resulting in an almost product geometry, revealing invariant scales like minimal length and maximal speed without breaking covariance.

Findings

Identification of an almost product structure in brane geometry

Emergence of invariant scales: minimal length and maximal speed

Manifestation of maximal acceleration effects at low energy

Abstract

Any candidate theory of quantum gravity must address the breakdown of the classical smooth manifold picture of space-time at distances comparable to the Planck length. String theory, in contrast, is formulated on conventional space-time. However, we show that in the low energy limit, the dynamics of generally curved Dirichlet p-branes possess an extended local isometry group, which can be absorbed into the brane geometry as an almost product structure. The induced kinematics encode two invariant scales, namely a minimal length and a maximal speed, without breaking general covariance. Quantum gravity effects on D-branes at low energy are then seen to manifest themselves by the kinematical effects of a maximal acceleration. Experimental and theoretical implications of such new kinematics are easily derived. We comment on consequences for brane world phenomenology.