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

Abstract

The Lorentz harmonic formulation of D-dimensional bosonic p-brane theory with D≥ (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. Hence it 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.