Abstract
We prove that, for every 6D supergravity theory that has an F-theory description, the property of charge completeness for the connected component of the gauge group (meaning that all charges in the corresponding charge lattice are realized by massive or massless states in the theory) is equivalent to a standard assumption made in F-theory for how geometry encodes the global gauge theory by means of the Mordell-Weil group of the elliptic fibration. This result also holds in 4D F-theory constructions for the parts of the gauge group that come from sections and from 7-branes. We find that in many 6D F-theory models the full charge lattice of the theory is generated by massless charged states; this occurs for each gauge factor where the associated anomaly coefficient satisfies a simple positivity condition. We describe many of the cases where this massless charge sufficiency condition holds, as well as exceptions where the positivity condition fails, and analyze the related global structure of the gauge group and associated Mordell-Weil torsion in explicit F-theory models.
Highlights
String theory, in its many avatars, gives rise to a wide range of vacuum solutions in various dimensions with a great variety of different gauge groups and matter content coupled to quantum gravity
We prove that, for every 6D supergravity theory that has an F-theory description, the property of charge completeness for the connected component of the gauge group is equivalent to a standard assumption made in F-theory for how geometry encodes the global gauge theory by means of the Mordell-Weil group of the elliptic fibration
We prove using Poincaré duality that for 6D N = (1, 0) supergravity theories that arise from F-theory, the charge completeness hypothesis for the connected component of the gauge group is equivalent to the standard assumption made in F-theory for how the global structure of the gauge group is encoded in geometry
Summary
In its many avatars, gives rise to a wide range of vacuum solutions in various dimensions with a great variety of different gauge groups and matter content coupled to quantum gravity. The set of 6D supergravity theories that can be realized through known string constructions essentially forms one large moduli space, with different branches connected by various kinds of geometric transitions.1 It was conjectured in [12] that, as in 10D, it may be possible to show that every quantum-consistent massless 6D supergravity spectrum is realized in string theory. In many of these theories we prove that the massless charges in the theory are sufficient to generate the full charge lattice, and explicitly describe the connection in these theories between Mordell-Weil torsion in the F-theory model and the fundamental group of the gauge group of the associated 6D supergravity theory. The automatic enhancement conjecture made in that paper is closely related in some cases to the massless charge sufficiency conjecture presented here, as discussed further in that paper; the analysis of that paper was inspired in part by some examples encountered in this work
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