The power of the F-theory and M-theory

Abstract

Recently, some evidence has emerged for the existence of a twelve dimensional formulation of type IIB strings, F-theory. Given a fact that F-theory exists, we make a proposal for a bosonic field theory in twelve dimensions that admits the bosonic sector of eleven-dimensional supergravity as a consistent truncation. It can also be consistently truncated to a ten-dimensional Lagrangian that contains all the BPS p-brane solitons of the type IIB theory. We have constructed multi-scalar, multi-center p-brane solutions in toroidally compactified M-theory. We use these solutions to show that all supersymmetric p-branes can be viewed as bound states of certain basic building blocks, namely p-branes that preserve 1/2 of the supersymmetry. We also explore the M-theory interpretation of p-branes in lower dimensions. We show that all the supersymmetric p-branes can be viewed as intersections of M-branes or boosted M-branes in D = 11. Using the ordinary Scherk-Schwarz dimensional reduction procedure, we have obtained the bosonic Lagrangian of N = 2, D = 9 supergravity theory by dimensionally reducing the eleven-dimensional Cremmer-Julia-Scherk (CJS) Lagrangian from eleven directly to nine dimensions. We constructed the N = 2, D = 9 supergravity theory up to the quartic fermionic terms and derive the supersymmetry transformation rules for the fields modulo cubic fermions. We consider a class of p-brane solutions of this theory, the stainless p-branes, which cannot be isotropically oxidized into higher dimensions. The new stainless elementary membrane and elementary particle solutions are found. It is explicitly verified that these solutions preserve half of the supersymmetry.