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

TL;DR

This paper explores how anomaly constraints shape the landscape of 6D quantum gravity theories and discusses their realization in string theory through F-theory, highlighting the role of geometric structures and potential exceptions to universality.

Contribution

It develops a global framework connecting 6D anomaly structures with F-theory geometry, advancing understanding of string universality and identifying possible constraints.

Findings

Anomaly structures determine integral lattices linked to Calabi-Yau three-folds.

F-theory geometry encodes gauge and matter data of 6D theories.

Potential exceptions suggest new constraints on quantum gravity models.

Abstract

Quantum anomalies, determined by the Atiyah-Singer index theorem, place strong constraints on the space of quantum gravity theories in six dimensions with minimal supersymmetry. The conjecture of "string universality" states that all such theories which do not have anomalies or other quantum inconsistencies are realized in string theory. This paper describes this conjecture and recent work by Kumar, Morrison, and the author towards developing a global picture of the space of consistent 6D supergravities and their realization in string theory via F-theory constructions. We focus on the discrete data for each model associated with the gauge symmetry group and the representation of this group on matter fields. The 6D anomaly structure determines an integral lattice for each gravity theory, which is related to the geometry of an elliptically fibered Calabi-Yau three-fold in an F-theory construction. Possible exceptions to the string universality conjecture suggest novel constraints on low-energy gravity theories which may be identified from the structure of F-theory geometry.