Some remarks on fundamental physical $F$-theory

Abstract

The purpose of this paper is to investigate the possibility of a physical 12-dimensional $F$-theory. We study the question of geometric interaction terms in the $F$-theory Lagrangians. We also introduce a new supergravity multiplet in dimension (9, 3) which is based on a particle with 3-dimensional time-like world volume. A construction of signature (9, 3) $F$-theory is given using dualities analogous to those considered by Hull, and possible matches of $F$-theory's low energy fields with the (9, 3)-supergravity field content are given. Finally, preliminary suggestions are made regarding a possible phenomenological compactification of $F$-theory from dimension (9, 3) to (3, 1).