An approach to F-theory

TL;DR

This paper explores BPS states in theories with two timelike dimensions, relating their algebraic structures to F-theory, and introduces new intersection rules for fundamental branes in twelve dimensions.

Contribution

It establishes a connection between BPS configurations in two-time theories and F-theory, providing a new algebraic framework and intersection rules for branes in twelve dimensions.

Findings

BPS states with two times have positive angular momentum, not energy.

The (10,2) superalgebra relates to F-theory through specific BPS configurations.

New intersection rules for 3-branes and 7-branes in twelve dimensions.

Abstract

We consider BPS configurations in theories with two timelike directions from the perspective of the supersymmetry algebra. We show that whereas a BPS state in a theory with one timelike variable must have positive energy, in a theory with two times any BPS state must have positive angular momentum in the timelike plane, in that $Z_{0\tilde{0}}>0$, where $0$ and $\tilde{0}$ are the two timelike directions. We consider some generic BPS solutions of theories with two timelike directions, and then specialise to the study of the (10,2) dimensional superalgebra for which the spinor operators generate 2-forms and 6-forms. We argue that the BPS configurations of this algebra relate to F-theory in the same way that the BPS configurations of the eleven dimensional supersymmetry algebra relate to M-theory. We show that the twelve dimensional theory is one of fundamental 3-branes and 7-branes, along with their dual partners. We then formulate the new intersection rules for these objects. Upon reduction of this system we find the algebraic description of the IIB-branes and the M-branes. Given these correspondences we may begin an algebraic study of F-theory.