Abstract
In this note we study the constraints on F-theory GUTs with extra U(1)'s in the context of elliptic fibrations with rational sections. We consider the simplest case of one abelian factor (Mordell–Weil rank one) and investigate the conditions that are induced on the coefficients of its Tate form. Converting the equation representing the generic hypersurface P112 to this Tate's form we find that the presence of a U(1), already in this local description, is consistent with the exceptional E6 and E7 non-abelian singularities. We briefly comment on a viable E6×U(1) effective F-theory model.
Highlights
It has been widely accepted that additional U (1) or discrete symmetries constitute an important ingredient in GUT model building
In this note we argue that the appearance of extra sections has significant implications on the engineering of non-abelian gauge symmetries based on the local Tate form of the model
In this note we investigated constraints on GUTs in F-theory compactifications with an extra rational section which corresponds to an additional abelian factor in the gauge group of the final effective theory model
Summary
It has been widely accepted that additional U (1) or discrete symmetries constitute an important ingredient in GUT model building. In this note we argue that the appearance of extra sections has significant implications on the engineering of non-abelian gauge symmetries based on the local Tate form of the model. We will see that such constraints make impossible the appearance of familiar groups such as SU(5) in the local Tate form To our knowledge, this issue has not been observed, and it might constitute another obstruction on the validity of simple Tate’s algorithm similar to those observed in reference [32]. In this note we show that in the context of the familiar local Tate’s algorithm, viable effective models based on the exceptional singularities can be still accommodated It is the purpose of this note to examine the aforementioned constraints and discuss the implications in the effective theory. We briefly discuss the spectrum of the model E6 × U (1)
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