Triples, fluxes, and strings

Abstract

We study string compactications with sixteen supersymmetries. The moduli space for these compactications becomes quite intricate in lower dimensions, partly because there are many dierent irreducible components. We focus primarily, but not exclusively, on compactications to seven or more dimensions. These vacua can be realized in a number ways: the perturbative constructions we study include toroidal compactications of the heterotic/type I strings, asymmetric orbifolds, and orientifolds. In addition, we describe less conventional M and F theory compactications on smooth spaces. The last class of vacua considered are compactications on singular spaces with non-trivial discrete fluxes. We nd a number of new components in the string moduli space. Contained in some of these components are M theory compactications with novel kinds of \frozen singularities. We are naturally led to conjecture the existence of new dualities relating spaces with dierent singular geometries and fluxes. As our study of these vacua unfolds, we also learn about additional topics including: F theory on spaces without section, automorphisms of del Pezzo surfaces, and novel physics (and puzzles) from equivariant K-theory. Lastly, we comment on how the data we gain about the M theory three-form might be interpreted.