1,851 research outputs found
U(n) Spectral Covers from Decomposition
We construct decomposed spectral covers for bundles on elliptically fibered
Calabi-Yau threefolds whose structure groups are S(U(1) x U(4)), S(U(2) x U(3))
and S(U(1) x U(1) x U(3)) in heterotic string compactifications. The
decomposition requires not only the tuning of the SU(5) spectral covers but
also the tuning of the complex structure moduli of the Calabi-Yau threefolds.
This configuration is translated to geometric data on F-theory side. We find
that the monodromy locus for two-cycles in K3 fibered Calabi-Yau fourfolds in a
stable degeneration limit is globally factorized with squared factors under the
decomposition conditions. This signals that the monodromy group is reduced and
there is a U(1) symmetry in a low energy effective field theory. To support
that, we explicitly check the reduction of a monodromy group in an appreciable
region of the moduli space for an gauge theory with (1+2) decomposition.
This may provide a systematic way for constructing F-theory models with U(1)
symmetries.Comment: 41 pages, 14 figures; v2: minor improvements and a reference adde
GUT theories from Calabi-Yau 4-folds with SO(10) Singularities
We consider an SO(10) GUT model from F-theory compactified on an elliptically
fibered Calabi-Yau with a D5 singularity. To obtain the matter curves and the
Yukawa couplings, we use a global description to resolve the singularity. We
identify the vector and spinor matter representations and their Yukawa
couplings and we explicitly build the G-fluxes in the global model and check
the agreement with the semi-local results. As our bundle is of type SU(2k),
some extra conditions need to be applied to match the fluxes.Comment: 27 page
Tate Form and Weak Coupling Limits in F-theory
We consider the weak coupling limit of F-theory in the presence of
non-Abelian gauge groups implemented using the traditional ansatz coming from
Tate's algorithm. We classify the types of singularities that could appear in
the weak coupling limit and explain their resolution. In particular, the weak
coupling limit of SU(n) gauge groups leads to an orientifold theory which
suffers from conifold singulaties that do not admit a crepant resolution
compatible with the orientifold involution. We present a simple resolution to
this problem by introducing a new weak coupling regime that admits
singularities compatible with both a crepant resolution and an orientifold
symmetry. We also comment on possible applications of the new limit to model
building. We finally discuss other unexpected phenomena as for example the
existence of several non-equivalent directions to flow from strong to weak
coupling leading to different gauge groups.Comment: 34 page
Gauge Fluxes in F-theory and Type IIB Orientifolds
We provide a detailed correspondence between G_4 gauge fluxes in F-theory
compactifications with SU(n) and SU(n)x(1) gauge symmetry and their Type IIB
orientifold limit. Based on the resolution of the relevant F-theory Tate models
we classify the factorisable G_4-fluxes and match them with the set of
universal D5-tadpole free U(1)-fluxes in Type IIB. Where available, the global
version of the universal spectral cover flux corresponds to Type IIB gauge flux
associated with a massive diagonal U(1). In U(1)-restricted Tate models extra
massless abelian fluxes exist which are associated with specific linear
combinations of Type IIB fluxes. Key to a quantitative match between F-theory
and Type IIB is a proper treatment of the conifold singularity encountered in
the Sen limit of generic F-theory models. We also shed further light on the
brane recombination process relating generic and U(1)-restricted Tate models.Comment: 53 pages, 3 figures; v2: Refs added; v3: minor corrections to match
version published in JHE
On Global Flipped SU(5) GUTs in F-theory
We construct an SU(4) spectral divisor and its factorization of types (3,1)
and (2,2) based on the construction proposed in [1]. We calculate the chiral
spectra of flipped SU(5) GUTs by using the spectral divisor construction. The
results agree with those from the analysis of semi-local spectral covers. Our
computations provide an example for the validity of the spectral divisor
construction and suggest that the standard heterotic formulae are applicable to
the case of F-theory on an elliptically fibered Calabi-Yau fourfold with no
heterotic dual.Comment: 45 pages, 12 tables, 1 figure; typos corrected, footnotes added, and
a reference adde
Evidence for F(uzz) Theory
We show that in the decoupling limit of an F-theory compactification, the
internal directions of the seven-branes must wrap a non-commutative four-cycle
S. We introduce a general method for obtaining fuzzy geometric spaces via toric
geometry, and develop tools for engineering four-dimensional GUT models from
this non-commutative setup. We obtain the chiral matter content and Yukawa
couplings, and show that the theory has a finite Kaluza-Klein spectrum. The
value of 1/alpha_(GUT) is predicted to be equal to the number of fuzzy points
on the internal four-cycle S. This relation puts a non-trivial restriction on
the space of gauge theories that can arise as a limit of F-theory. By viewing
the seven-brane as tiled by D3-branes sitting at the N fuzzy points of the
geometry, we argue that this theory admits a holographic dual description in
the large N limit. We also entertain the possibility of constructing string
models with large fuzzy extra dimensions, but with a high scale for quantum
gravity.Comment: v2: 66 pages, 3 figures, references and clarifications adde
Wavefunctions and the Point of E8 in F-theory
In F-theory GUTs interactions between fields are typically localised at
points of enhanced symmetry in the internal dimensions implying that the
coefficient of the associated operator can be studied using a local
wavefunctions overlap calculation. Some F-theory SU(5) GUT theories may exhibit
a maximum symmetry enhancement at a point to E8, and in this case all the
operators of the theory can be associated to the same point. We take initial
steps towards the study of operators in such theories. We calculate
wavefunctions and their overlaps around a general point of enhancement and
establish constraints on the local form of the fluxes. We then apply the
general results to a simple model at a point of E8 enhancement and calculate
some example operators such as Yukawa couplings and dimension-five couplings
that can lead to proton decay.Comment: 46 page
Flipped SU(5) GUTs from E_8 Singularities in F-theory
In this paper we construct supersymmetric flipped SU(5) GUTs from E_8
singularities in F-theory. We start from an SO(10) singularity unfolded from an
E_8 singularity by using an SU(4) spectral cover. To obtain realistic models,
we consider (3,1) and (2,2) factorizations of the SU(4) cover. After turning on
the massless U(1)_X gauge flux, we obtain the SU(5) X U(1)_X gauge group. Based
on the well-studied geometric backgrounds in the literature, we demonstrate
several models and discuss their phenomenology.Comment: 46 pages, 23 tables, 1 figure, typos corrected, references added, and
new examples presente
Abelian Gauge Fluxes and Local Models in F-Theory
We analyze the Abelian gauge fluxes in local F-theory models with G_S=SU(6)
and SO(10). For the case of G_S=SO(10), there is a no-go theorem which states
that for an exotic-free spectrum, there are no solutions for U(1)^2 gauge
fluxes. We explicitly construct the U(1)^2 gauge fluxes with an exotic-free
bulk spectrum for the case of G_S=SU(6). We also analyze the conditions for the
curves supporting the given field content and discuss non-minimal spectra of
the MSSM with doublet-triplet splitting.Comment: 43 pages, 15 tables; typos corrected, reference adde
Rational F-Theory GUTs without exotics
We construct F-theory GUT models without exotic matter, leading to the MSSM
matter spectrum with potential singlet extensions. The interplay of engineering
explicit geometric setups, absence of four-dimensional anomalies, and realistic
phenomenology of the couplings places severe constraints on the allowed local
models in a given geometry. In constructions based on the spectral cover we
find no model satisfying all these requirements. We then provide a survey of
models with additional U(1) symmetries arising from rational sections of the
elliptic fibration in toric constructions and obtain phenomenologically
appealing models based on SU(5) tops. Furthermore we perform a bottom-up
exploration beyond the toric section constructions discussed in the literature
so far and identify benchmark models passing all our criteria, which can serve
as a guideline for future geometric engineering.Comment: 27 Pages, 1 Figur
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