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 F-theory 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.
Highlights
Six-dimensional supergravity is a promising arena in which to understand the relationship between possible low-energy theories of quantum gravity and UV completions in the context of string theory
We have analyzed a variety of constructions for specific gauge groups G that satisfy the conditions of the Automatic Enhancement Conjecture stated in section 2 that there is a containing theory G, M such that the larger theory cannot be broken down to the smaller theory with gauge group G by a supersymmetry-preserving Higgs deformation
For each of the specific gauge groups G with generic matter content, we have used explicit constructions of universal Weierstrass models to identify positivity conditions and associated local conditions in terms of anomaly coefficients that are sufficient to show that certain gauge group and matter combinations cannot be realized in F-theory without some additional enhanced gauge factors
Summary
Six-dimensional supergravity is a promising arena in which to understand the relationship between possible low-energy theories of quantum gravity and UV completions in the context of string theory. It was conjectured in [14] that string universality should hold for the massless spectra of 6D supergravity theories, so that any massless spectrum associated with a supersymmetric theory of gauge fields and gravity not realized in string or F-theory should be provably inconsistent At this point in time, despite ongoing progress both in understanding the range of possible F-theory constructions and in identifying new quantum consistency conditions for 6D supergravity theories, there are still many theories, including some infinite classes of theories, in the apparent swampland [15]1 of 6D low-energy supergravity theories that obey anomaly cancellation as well as all other known quantum consistency conditions and yet have no known F-theory realization. The work in this paper is complemented by a separate but related work nearing completion [19] that addresses questions of completeness of the charge spectra and massless charge spectra in 6D supergravity theories and their F-theory realizations
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