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

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. Quick review of 6D supergravity and F-theory realizationsWe begin by briefly reviewing the structure of 6D N = (1, 0) supergravity theories and their realizations in F-theory

Jacobian Calabi-Yau 3-fold and charge completeness in six-dimensional theory

“…Related to the swampland and 6D N = (1, 0) supergravity theories, very interesting aspects of charge completeness 3 were studied in a recent study by Morrison and Taylor [24]. They showed in [24] that for 6D F-theory models, the property of charge completeness 1 Reviews of the swampland criteria can be found in [4,5]. 2 Recent studies have investigated gauge groups formed in F-theory, for example [9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25].…”

“…They showed in [24] that for 6D F-theory models, the property of charge completeness 1 Reviews of the swampland criteria can be found in [4,5]. 2 Recent studies have investigated gauge groups formed in F-theory, for example [9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25]. 3 The notion of the charge completeness was discussed by the authors in [26].…”

“…Fibers of the elliptic fibration are generically elliptic curves, and the modular parameter of the elliptic fibers is identified with axiodilaton in type IIB superstring theory. The "standard assumption" in F-theory [28,29,30] states [24] that the geometry of the elliptic fibration as a compactification space encodes the global structure of the gauge group.…”

“…The gauge group formed in the 6D theory is denoted by G, and we use G 0 to denote the connected part of the gauge group G to line up with the notations in [24]. We use G 0 to represent the simply connected non-Abelian part of G. Given a 6D N = (1, 0) supergravity theory, which is realized as a 6D N = (1, 0) F-theory on an elliptically fibered Calabi-Yau 3fold and the elliptic fibration has the Mordell-Weil group ∼ = Z n ⊕Tor(M W ) (where Tor(M W ) represents the Mordell-Weil torsion), the standard assumption in F-theory [28,29,30] states that the connected part G 0 is given as the quotient G 0 = (G 0 × U (1) n )/H, where H satisfies the relation H ∩ G 0 = Tor(M W ), and Tor(π 1 (G)) coincides with the Mordell-Weil torsion Tor(M W ).…”

Four-dimensional $\mathcal{N}=1$ SCFTs on S-folds with T-branes and AdS/CFT correspondence

“…The field has been intensively studied since this progress, e.g., in[17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40] 2. There have been various efforts to analyze gauge groups formed in F-theory, e.g., in[45,46,47,48,49,50,51,52,53,54,55,56,57].…”