GUT theories from Calabi-Yau 4-folds with SO(10) singularities

Abstract:We initiate the construction of gauge fluxes in F-theory compactifications on genus-one fibrations which only have a multi-section as opposed to a section. F-theory on such spaces gives rise to discrete gauge symmetries in the effective action. We generalize the transversality conditions on gauge fluxes known for elliptic fibrations by taking into account the properties of the available multi-section. We test these general conditions by constructing all vertical gauge fluxes in a bisection model with gauge group SU(5)×Z 2 . The non-abelian anomalies are shown to vanish. These flux solutions are dynamically related to fluxes on a fibration with gauge group SU(5)×U(1) by a conifold transition. Considerations of flux quantization reveal an arithmetic constraint on certain intersection numbers on the base which must necessarily be satisfied in a smooth geometry. Combined with the proposed transversality conditions on the fluxes these conditions are shown to imply cancellation of the discrete Z 2 gauge anomalies as required by general consistency considerations.

Section: Jhep01(2016)098mentioning

confidence: 99%

Fluxes in F-theory compactifications on genus-one fibrations

Lin

Mayrhofer

Till

et al. 2016

“…The resolution of SO(10) was done in [31], however as for SU (5) we present it in the framework of the current paper, so as to have one explicit example using the general analysis for SO(4k + 2) with k = 2. Furthermore, the low k cases exhibit some pathologies, which will be explained.…”

Section: B2 So(10)mentioning

confidence: 99%

“…Resolutions of singularities for some low gauge group relevant for GUT models have been studied in the literature: for SU(5) in [8,9], for E 6 and SO(10) codimension 1 singularities, the resolution of CY fourfolds has appeared in [30,31], and for other models related to the SU(5) case, e.g. with additional U(1) factors and connection to orientifold limits, the resolved geometries were studied in [27,29,[32][33][34][35][36][37].…”

Section: Introductionmentioning

confidence: 99%

The Tate form on steroids: resolution and higher codimension fibers

Lawrie

Schäfer‐Nameki

2013

147

F-theory on singular elliptically fibered Calabi-Yau four-folds provides a setting to geometrically study four-dimensional N = 1 supersymmetric gauge theories, including matter and Yukawa couplings. The gauge degrees of freedom arise from the codimension 1 singular loci, the matter and Yukawa couplings are generated at enhanced singularities in higher codimension. We construct the resolution of the singular Tate form for an elliptic Calabi-Yau four-fold with an ADE type singularity in codimension 1 and study the structure of the fibers in codimension 2 and 3. We determine the fibers in higher codimension which in general are of Kodaira type along minimal singular loci, and are thus consistent with the low energy gauge-theoretic intuition. Furthermore, we provide a complementary description of the fibers in higher codimension, which will also be applicable to non-minimal singularities. The irreducible components in the fiber in codimension 2 correspond to weights of representations of the ADE gauge group. These can split further in codimension 3 in a way that is consistent with the generation of Yukawa couplings. Applying this reasoning, we then venture out to study non-minimal singularities, which occur for A type along codimension 3, and for D and E also in codimension 2. The fibers in this case are non-Kodaira, however some insight into these singularities can be gained by considering the splitting of fiber components along higher codimension, which are shown to be consistent with matter and Yukawa couplings for the corresponding gauge groups.

“…Indeed only the simplest SU(5) GUTs can in principle avoid exotic matter in the spectrum [4]. However, by considering different fluxes, other models have been constructed with different GUT groups, such as SO (10) and E 6 [20][21][22][23][24]. In particular, it is possible to achieve gauge coupling unification from E 6 in the presence of TeV scale exotics originating from both the matter curves and the bulk [25].…”

Section: Jhep09(2014)107mentioning

confidence: 99%

Discrete family symmetry from F-theory GUTs

Karozas

King

Leontaris

et al. 2014

We consider realistic F-theory GUT models based on discrete family symmetries A 4 and S 3 , combined with SU(5) GUT, comparing our results to existing field theory models based on these groups. We provide an explicit calculation to support the emergence of the family symmetry from the discrete monodromies arising in F-theory. We work within the spectral cover picture where in the present context the discrete symmetries are associated to monodromies among the roots of a five degree polynomial and hence constitute a subgroup of the S 5 permutation symmetry. We focus on the cases of A 4 and S 3 subgroups, motivated by successful phenomenological models interpreting the fermion mass hierarchy and in particular the neutrino data. More precisely, we study the implications on the effective field theories by analysing the relevant discriminants and the topological properties of the polynomial coefficients, while we propose a discrete version of the doublet-triplet splitting mechanism.