Towards Exotic Matter and Discrete Non-Abelian Symmetries in F-theory

Abstract

We present a prescription in F-theory for realizing matter in "exotic" representations of product gauge groups. For 6D vacua, bifundamental hypermultiplets are engineered by starting at a singular point in moduli space which includes 6D superconformal field theories coupled to gravity. A deformation in Higgs branch moduli space takes us to a weakly coupled gauge theory description. In the corresponding elliptically fibered Calabi-Yau threefold, the minimal Weierstrass model parameters (f, g, ∆) vanish at collisions of the discriminant at least to order (4, 6, 12), but with sufficiently high order of tangency to ensure the existence of T-brane deformations to a weakly coupled gauge theory with exotic bifundamentals. We present explicit examples including bifundamental hypermultiplets of e 7 × su 2 and e 6 × su 3 , each of which have dual heterotic orbifold descriptions. Geometrically, these matter fields are delocalized across multiple points of an F-theory geometry. Symmetry breaking with such representations can be used to produce high dimension representations of simple gauge groups such as the four-index symmetric representation of su 2 and the three-index symmetric representation of su 3 , and after further higgsing can yield discrete non-abelian symmetries.

Fission, fusion, and 6D RG flows

“…Given a nilpotent element µ ∈ g flav , there is a corresponding su(2) algebra, as defined by µ, µ † and the commutator [µ, µ † ]. Even though a nilpotent element defines a T-brane deformation 3 of the SCFT [8] (see also [20,22,42]), the commutator [µ, µ † ] is also a generator in the Cartan subalgebra, and can therefore be identified with some unfolding of the singularity. 4 For classical flavor symmetry algebras of su, so, sp-type, we can label an orbit by a partition of integers [µ a 1 1 , ..., µ a k k ], where we take µ 1 > ... > µ k , and a i > 0 indicates the multiplicity of a given integer.…”

“…For a partial list of references to T-branes in F-theory see e.g [31][32][33][34][35][36][37][38][39][40][41][42]4.…”

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

“…While these models have (4,6) points corresponding to SCFTs coupled to the SO( 7) and E 7 factors, the analysis of Kimura suggests that interpreting these loci as bi-charged matter may nonetheless give solutions to the anomaly cancellation conditions. The notion that (56, 2) matter transforming under E 7 × SU (2) may be realized in F-theory at apparent superconformal loci was also considered previously in [89]. As pointed out there, the existence of a heterotic dual with such matter suggests that there is a sensible interpretation of these constructions in the F-theory context.…”

Nilpotent networks and 4D RG flows

“…The nilpotent case is especially interesting because it is essentially "invisible" to the complex geometry of the model. We can then view the mass parameters m adj as background values for Φ (2,0) [10,9], and the particular case of a nilpotent mass deformation defines a T-brane configuration [31,32,11,[33][34][35][36][37][38][39][40][41].…”

“…The string theory interpretation of nilpotent deformations is also quite interesting, as they are associated with T-brane configurations of 7-branes (see e.g. [31,32,11,[33][34][35][36][37][38][39][40][41]), namely they leave intact the Weierstrass model of the associated F-theory geometry, but nevertheless deform the physical theory.…”