87 research outputs found
Non-Abelian Brane Worlds: The Heterotic String Story
We discuss chiral supersymmetric compactifications of the SO(32) heterotic
string on Calabi-Yau manifolds equipped with direct sums of stable bundles with
structure group U(n). In addition we allow for non-perturbative heterotic
five-branes. These models are S-dual to Type I compactifications with D9- and
D5-branes, which by themselves are mirror symmetric to general intersecting
D6-brane models. For the construction of concrete examples we consider
elliptically fibered Calabi-Yau manifolds with SU(n) bundles given by the
spectral cover construction. The U(n) bundles are obtained via twisting by line
bundles. We present a four-generation Pati-Salam and a three-generation
Standard-like model.Comment: 29 pages, 7 tables, LATEX; v2: refs adde
One in a Billion: MSSM-like D-Brane Statistics
Continuing our recent work hep-th/0411173, we study the statistics of
four-dimensional, supersymmetric intersecting D-brane models in a toroidal
orientifold background. We have performed a vast computer survey of solutions
to the stringy consistency conditions and present their statistical
implications with special emphasis on the frequency of Standard Model features.
Among the topics we discuss are the implications of the K-theory constraints,
statistical correlations among physical quantities and an investigation of the
various statistical suppression factors arising once certain Standard Model
features are required. We estimate the frequency of an MSSM like gauge group
with three generations to be one in a billion.Comment: 36 pages, 12 figures; v2: typos corrected, one ref. added; v3: minor
changes, version to appear in JHE
Yukawa couplings and masses of non-chiral states for the Standard Model on D6-branes on T6/Z6'
The perturbative leading order open string three-point couplings for the
Standard Model with hidden USp(6) on fractional D6-branes on T6/Z6' from
arXiv:0806.3039 [hep-th], arXiv:0910.0843 [hep-th] are computed. Physical
Yukawa couplings consisting of holomorphic Wilsonian superpotential terms times
a non-holomorphic prefactor involving the corresponding classical open string
Kaehler metrics are given, and mass terms for all non-chiral matter states are
derived. The lepton Yukawa interactions are at leading order flavour diagonal,
while the quark sector displays a more intricate pattern of mixings. While N=2
supersymmetric sectors acquire masses via only two D6-brane displacements -
which also provide the hierarchies between up- and down-type Yukawas within one
quark or lepton generation -, the remaining vector-like states receive masses
via perturbative three-point couplings to some Standard Model singlet fields
with vevs along flat directions. Couplings to the hidden sector and messengers
for supersymmetry breaking are briefly discussed.Comment: 52 pages (including 8p. appendix); 5 figures; 14 tables; v2:
discussion in section 4.1.3 extended, footnote 5 added, typos corrected,
accepted by JHE
Massive Abelian Gauge Symmetries and Fluxes in F-theory
F-theory compactified on a Calabi-Yau fourfold naturally describes
non-Abelian gauge symmetries through the singularity structure of the elliptic
fibration. In contrast Abelian symmetries are more difficult to study because
of their inherently global nature. We argue that in general F-theory
compactifications there are massive Abelian symmetries, such as the uplift of
the Abelian part of the U(N) gauge group on D7-branes, that arise from
non-Kahler resolutions of the dual M-theory setup. The four-dimensional
F-theory vacuum with vanishing expectation values for the gauge fields
corresponds to the Calabi-Yau limit. We propose that fluxes that are turned on
along these U(1)s are uplifted to non-harmonic four-form fluxes. We derive the
effective four-dimensional gauged supergravity resulting from F-theory
compactifications in the presence of the Abelian gauge factors including the
effects of possible fluxes on the gauging, tadpoles and matter spectrum.Comment: 49 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 Flux Quantization in F-Theory II: Unitary and Symplectic Gauge Groups
We study the quantization of the M-theory G-flux on elliptically fibered
Calabi-Yau fourfolds with singularities giving rise to unitary and symplectic
gauge groups. We seek and find its relation to the Freed-Witten quantization of
worldvolume fluxes on 7-branes in type IIB orientifold compactifications on
Calabi-Yau threefolds. By explicitly constructing the appropriate four-cycles
on which to calculate the periods of the second Chern class of the fourfolds,
we find that there is a half-integral shift in the quantization of G-flux
whenever the corresponding dual 7-brane is wrapped on a non-spin submanifold.
This correspondence of quantizations holds for all unitary and symplectic gauge
groups, except for SU(3), which behaves mysteriously. We also perform our
analysis in the case where, in addition to the aforementioned gauge groups,
there is also a 'flavor' U(1)-gauge group.Comment: 33 pages, 4 figure
Toric Construction of Global F-Theory GUTs
We systematically construct a large number of compact Calabi-Yau fourfolds
which are suitable for F-theory model building. These elliptically fibered
Calabi-Yaus are complete intersections of two hypersurfaces in a six
dimensional ambient space. We first construct three-dimensional base manifolds
that are hypersurfaces in a toric ambient space. We search for divisors which
can support an F-theory GUT. The fourfolds are obtained as elliptic fibrations
over these base manifolds. We find that elementary conditions which are
motivated by F-theory GUTs lead to strong constraints on the geometry, which
significantly reduce the number of suitable models. The complete database of
models is available at http://hep.itp.tuwien.ac.at/f-theory/. We work out
several examples in more detail.Comment: 35 pages, references adde
Unification, KK-thresholds and the top Yukawa coupling in F-theory GUTs
In a class of F-theory SU(5) GUTs the low energy chiral mass spectrum is
obtained from rank one fermion mass textures with a hierarchical structure
organised by U(1) symmetries embedded in the exceptional E_8 group. In these
theories chiral fields reside on matter `curves' and the tree level masses are
computed from integrals of overlapping wavefuctions of the particles at the
triple intersection points. This calculation requires knowledge of the exact
form of the wavefuctions. In this work we propose a way to obtain a reliable
estimate of the various quantities which determine the strength of the Yukawa
couplings. We use previous analysis of KK threshold effects to determine the
(ratios of) heavy mass scales of the theory which are involved in the
normalization of the wave functions. We consider similar effects from the
chiral spectrum of these models and discuss possible constraints on the
emerging matter content. In this approach, we find that the Yukawa couplings
can be determined solely from the U(1) charges of the states in the
`intersection' and the torsion which is a topological invariant quantity. We
apply the results to a viable SU(5) model with minimal spectrum which satisfies
all the constraints imposed by our analysis. We use renormalization group
analysis to estimate the top and bottom masses and find that they are in
agreement with the experimental values.Comment: 28 pages, 2 figure
On Flux Quantization in F-Theory
We study the problem of four-form flux quantization in F-theory
compactifications. We prove that for smooth, elliptically fibered Calabi-Yau
fourfolds with a Weierstrass representation, the flux is always integrally
quantized. This implies that any possible half-integral quantization effects
must come from 7-branes, i.e. from singularities of the fourfold. We
subsequently analyze the quantization rule on explicit fourfolds with Sp(N)
singularities, and connect our findings via Sen's limit to IIB string theory.
Via direct computations we find that the four-form is half-integrally quantized
whenever the corresponding 7-brane stacks wrap non-spin complex surfaces, in
accordance with the perturbative Freed-Witten anomaly. Our calculations on the
fourfolds are done via toric techniques, whereas in IIB we rely on Sen's
tachyon condensation picture to treat bound states of branes. Finally, we give
general formulae for the curvature- and flux-induced D3 tadpoles for general
fourfolds with Sp(N) singularities.Comment: 46 page
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