Abstract
We show that massless fields with large abelian charges (up to at least q = 21) can be constructed in 6D F-theory models with a U(1) gauge group. To show this, we explicitly construct F-theory Weierstrass models with nonabelian gauge groups that can be broken to U(1) theories with a variety of large charges. Determining the maximum abelian charge allowed in such a theory is key to eliminating what seems currently to be an infinite swampland of apparently consistent U(1) supergravity theories with large charges.
Highlights
In six dimensions, for supersymmetric theories of gravity with nonabelian gauge groups, there are strong constraints on the possible matter representations that can arise
We consider possible charges for massless fields charged under a gauge group in a 6D supergravity theory that has only a single U(1) factor, like the familiar four-dimensional theory of electromagnetism
For theories with fewer than 9 tensor multiplets, anomaly cancellation conditions alone restrict the set of possible nonabelian gauge groups and charged matter fields to a finite set [5, 15]
Summary
One would establish that a certain charge can be realized in F-theory by finding an explicit U(1) model admitting the desired charge. The currently known F-theory models with just a U(1) gauge group only admit charges ±1 through ±4, and there are few, if any, tractable techniques available for systematically constructing models with arbitrarily large charges. Given these difficulties, we use an indirect approach to determine that any other specific charges must be realized in F-theory. We will not be able to establish an upper bound on the charges in F-theory This technique demonstrates that the highest possible charge must be at least ±21, significantly larger than the charges that have currently been realized in explicit F-theory models. We are interested in starting with a theory having a gauge group SU(N ) and at least two matter fields in the adjoint representation, which can be broken by Higgsing processes down to a theory with a U(1) gauge group and various charged matter representations
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