Automatic Enhancement in 6D Supergravity and F-theory Models

Abstract

We observe that in many F-theory models, tuning a specific gauge group G and matter content M under certain circumstances leads to an automatic enhancement to a larger gauge group G ⊃ G and matter content M ⊃ M . We propose that this is true for any theory G, M whenever there exists a containing theory G , M that cannot be Higgsed down to G, M . We give a number of examples including non-Higgsable gauge factors, nonabelian gauge factors, abelian gauge factors, and exotic matter. In each of these cases, tuning an Ftheory model with the desired features produces either an enhancement or an inconsistency, often when the associated anomaly coefficient becomes too large. This principle applies to a variety of models in the apparent 6D supergravity swampland, including some of the simplest cases with U(1) and SU(N ) gauge groups and generic matter, as well as infinite families of U(1) models with higher charges presented in the prior literature, potentially ruling out all these apparent swampland theories.

Orders of Vanishing and U(1) Charges in F-theory

“…(2) m associated with P should have p-adic valuations given by an elliptic troublemaker sequence: 28 v p (W (2) m ) = R m (a, l) .…”

“…• The models involving u(1) factors in [28], including the su(18) ⊕ u(1) and su(19) ⊕ u(1) models. While these models were not analyzed using resolutions, the matter spectra given there, which can be recovered with the techniques presented here, agree with the anomaly cancellation conditions and the expectations from Higgsing related nonabelian models.…”

“…Only a finite number of these matter spectra can be realized in F-theory models [27], presenting the possibility of an infinite swampland of such models. (See [28] for recent developments regarding some of these infinite families. )…”

Charge completeness and the massless charge lattice in F-theory models of supergravity

“…[12]) gives many insights into these theories, but at this time there are still substantial classes of apparently consistent 6D supergravity theories without an F-theory realization; for example, there is an infinite class of theories with no tensor multiplets, a single U(1) gauge factor, and matter fields with arbitrarily large U(1) charges that cannot be realized in F-theory but that satisfy anomaly cancellation and all other known quantum consistency conditions on low-energy 6D field theories coupled to gravity [13]. Other aspects of the 6D supergravity swampland have been explored in a variety of papers, including [5,10,[14][15][16][17][18][19].…”

“…In [30] related aspects of the global structure of the gauge group for 8D F-theory models have been investigated. In [18], a general characterization is given of a large set of 6D supergravity models that appear to be compatible with known quantum consistency conditions but lack an F-theory realization. Such models violate an automatic enhancement condition that seems to hold for all theories that come from F-theory.…”