15 research outputs found
B-L Cosmic Strings in Heterotic Standard Models
E_{8} X E_{8} heterotic string and M-theory, when compactified on smooth
Calabi-Yau manifolds with SU(4) vector bundles, can give rise to softly broken
N=1 supersymmetric theories with the exact matter spectrum of the MSSM,
including three right-handed neutrinos and one Higgs-Higgs conjugate pair of
supermultiplets. These vacua have the SU(3)_{C} X SU(2)_{L} X U(1)_{Y} gauge
group of the standard model augmented by an additional gauged U(1)_{B-L}. Their
minimal content requires that the B-L symmetry be spontaneously broken by a
vacuum expectation value of at least one right-handed sneutrino. The soft
supersymmetry breaking operators can induce radiative breaking of the B-L gauge
symmetry with an acceptable B-L/electroweak hierarchy. In this paper, it is
shown that U(1)_{B-L} cosmic strings occur in this context, potentially with
both bosonic and fermionic superconductivity. We present a numerical analysis
that demonstrates that boson condensates can, in principle, form for theories
of this type. However, the weak Yukawa and gauge couplings of the right-handed
sneutrino suggests that bosonic superconductivity will not occur in the
simplest vacua in this context. The electroweak phase transition also disallows
fermion superconductivity, although substantial bound state fermion currents
can exist.Comment: 41 pages, 5 figure
Numerical Hermitian Yang-Mills Connections and Vector Bundle Stability in Heterotic Theories
A numerical algorithm is presented for explicitly computing the gauge
connection on slope-stable holomorphic vector bundles on Calabi-Yau manifolds.
To illustrate this algorithm, we calculate the connections on stable monad
bundles defined on the K3 twofold and Quintic threefold. An error measure is
introduced to determine how closely our algorithmic connection approximates a
solution to the Hermitian Yang-Mills equations. We then extend our results by
investigating the behavior of non slope-stable bundles. In a variety of
examples, it is shown that the failure of these bundles to satisfy the
Hermitian Yang-Mills equations, including field-strength singularities, can be
accurately reproduced numerically. These results make it possible to
numerically determine whether or not a vector bundle is slope-stable, thus
providing an important new tool in the exploration of heterotic vacua.Comment: 52 pages, 15 figures. LaTex formatting of figures corrected in
version 2
Flavor Structure in F-theory Compactifications
F-theory is one of frameworks in string theory where supersymmetric grand
unification is accommodated, and all the Yukawa couplings and Majorana masses
of right-handed neutrinos are generated. Yukawa couplings of charged fermions
are generated at codimension-3 singularities, and a contribution from a given
singularity point is known to be approximately rank 1. Thus, the approximate
rank of Yukawa matrices in low-energy effective theory of generic F-theory
compactifications are minimum of either the number of generations N_gen = 3 or
the number of singularity points of certain types. If there is a geometry with
only one E_6 type point and one D_6 type point over the entire 7-brane for
SU(5) gauge fields, F-theory compactified on such a geometry would reproduce
approximately rank-1 Yukawa matrices in the real world. We found, however, that
there is no such geometry. Thus, it is a problem how to generate hierarchical
Yukawa eigenvalues in F-theory compactifications. A solution in the literature
so far is to take an appropriate factorization limit. In this article, we
propose an alternative solution to the hierarchical structure problem (which
requires to tune some parameters) by studying how zero mode wavefunctions
depend on complex structure moduli. In this solution, the N_gen x N_gen CKM
matrix is predicted to have only N_gen entries of order unity without an extra
tuning of parameters, and the lepton flavor anarchy is predicted for the lepton
mixing matrix. We also obtained a precise description of zero mode
wavefunctions near the E_6 type singularity points, where the up-type Yukawa
couplings are generated.Comment: 148 page
Stabilizing the Complex Structure in Heterotic Calabi-Yau Vacua
In this paper, we show that the presence of gauge fields in heterotic
Calabi-Yau compacitifications causes the stabilisation of some, or all, of the
complex structure moduli of the Calabi-Yau manifold while maintaining a
Minkowski vacuum. Certain deformations of the Calabi-Yau complex structure,
with all other moduli held fixed, can lead to the gauge bundle becoming
non-holomorphic and, hence, non-supersymmetric. This leads to an F-term
potential which stabilizes the corresponding complex structure moduli. We use
10- and 4-dimensional field theory arguments as well as a derivation based
purely on algebraic geometry to show that this picture is indeed correct. An
explicit example is presented in which a large subset of complex structure
moduli is fixed. We demonstrate that this type of theory can serve as the
hidden sector in heterotic vacua and can co-exist with realistic particle
physics.Comment: 17 pages, Late
6D Effective Action of Heterotic Compactification on K3 with nontrivial Gauge Bundles
We compute the six-dimensional effective action of the heterotic string
compactified on K3 for the standard embedding and for a class of backgrounds
with line bundles and appropriate Yang-Mills fluxes. We compute the couplings
of the charged scalars and the bundle moduli as functions of the geometrical K3
moduli from a Kaluza-Klein analysis. We derive the D-term potential and show
that in the flux backgrounds U(1) vector multiplets become massive by a
Stuckelberg mechanism.Comment: 41 pages, typos corrected, references adde
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
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
The Worldvolume Action of Kink Solitons in AdS Spacetime
A formalism is presented for computing the higher-order corrections to the
worldvolume action of co-dimension one solitons. By modifying its potential, an
explicit "kink" solution of a real scalar field in AdS spacetime is found. The
formalism is then applied to explicitly compute the kink worldvolume action to
quadratic order in two expansion parameters--associated with the hypersurface
fluctuation length and the radius of AdS spacetime respectively. Two
alternative methods are given for doing this. The results are expressed in
terms of the trace of the extrinsic curvature and the intrinsic scalar
curvature. In addition to conformal Galileon interactions, we find a
non-Galileon term which is never sub-dominant. This method can be extended to
any conformally flat bulk spacetime.Comment: 32 pages, 3 figures, typos corrected and additional comments adde