String-Like Description of Gravity and Possible Applications for F-theory

TL;DR

This paper explores a string-like formulation of gravity using p-brane models coupled with antisymmetric tensor fields, with potential applications to F-theory's bosonic geometry and new theoretical insights.

Contribution

It introduces a Lorentz harmonic formulation of p-brane theory that models gravity as a string-like object, extending the Regge-Teitelboim idea and applying it to F-theory contexts.

Findings

Models describe gravity as a minimal surface embedded in higher dimensions

Application to D=2+10 and d=2+2 geometries relevant for F-theory

Speculative insights into bosonic sector of F-theory from p-brane dynamics

Abstract

The Lorentz harmonic formulation of D-dimensional bosonic p-brane theory with $D\geq (p+1)(p+2)/2$ coupled to an antisymmetric tensor field of rank d=(p+1) provides the dynamical ground for the description of d=(p+1) dimensional Gravity. It hence realizes the idea of Regge and Teitelboim on a 'string-like' description of gravity. The simplest nontrivial models of such a kind are provided by free D-dimensional p-branes in which world volumes are embedded as minimal surfaces. Possible applications of such a model with d=2+2 and D=2+10 for studying a geometry of bosonic sector of F-theory are considered. Some speculations inspired by the proposed model are presented.