Anomaly constraints and string/F-theory geometry in 6D quantum gravity

Abstract

Quantum anomalies, determined by the Atiyah-Singer in- dex theorem, place strong constraints on the space of quantu m gravity theories in six dimensions with minimal supersymmetry. The conjecture of “string universality” states that all such theories whic h do not have anomalies or other quantum inconsistencies are realized in string theory. This paper describes this conjecture and recent work by Kuma r, Mor- rison, and the author towards developing a global picture of the space of consistent 6D supergravities and their realization in st ring theory via F-theory constructions. We focus on the discrete data for ea ch model associated with the gauge symmetry group and the representa tion of this group on matter fields. The 6D anomaly structure determi nes an integral lattice for each gravity theory, which is related t o the geometry of an elliptically fibered Calabi-Yau three-fold in an F-the ory construc- tion. Possible exceptions to the string universality conje cture suggest novel constraints on low-energy gravity theories which may be identified from the structure of F-theory geometry