258 research outputs found
The Exact MSSM Spectrum from String Theory
We show the existence of realistic vacua in string theory whose observable
sector has exactly the matter content of the MSSM. This is achieved by
compactifying the E_8 x E_8 heterotic superstring on a smooth Calabi-Yau
threefold with an SU(4) gauge instanton and a Z_3 x Z_3 Wilson line.
Specifically, the observable sector is N=1 supersymmetric with gauge group
SU(3)_C x SU(2)_L x U(1)_Y x U(1)_{B-L}, three families of quarks and leptons,
each family with a right-handed neutrino, and one Higgs-Higgs conjugate pair.
Importantly, there are no extra vector-like pairs and no exotic matter in the
zero mode spectrum. There are, in addition, 6 geometric moduli and 13 gauge
instanton moduli in the observable sector. The holomorphic SU(4) vector bundle
of the observable sector is slope-stable.Comment: 15 pages, LaTeX; v2: Hidden sector is unstable, symbol typesetting
error corrected, clarifications and references added; v3: New discussion of
hidden secto
The Moduli of Reducible Vector Bundles
A procedure for computing the dimensions of the moduli spaces of reducible,
holomorphic vector bundles on elliptically fibered Calabi-Yau threefolds X is
presented. This procedure is applied to poly-stable rank n+m bundles of the
form V + pi* M, where V is a stable vector bundle with structure group SU(n) on
X and M is a stable vector bundle with structure group SU(m) on the base
surface B of X. Such bundles arise from small instanton transitions involving
five-branes wrapped on fibers of the elliptic fibration. The structure and
physical meaning of these transitions are discussed.Comment: 33+1 page
Electronic structures of GaAs/AlxGa1-xAs quantum double rings
In the framework of effective mass envelope function theory, the electronic structures of GaAs/AlxGa1-xAs quantum double rings (QDRs) are studied. Our model can be used to calculate the electronic structures of quantum wells, wires, dots, and the single ring. In calculations, the effects due to the different effective masses of electrons and holes in GaAs and AlxGa1-xAs and the valence band mixing are considered. The energy levels of electrons and holes are calculated for different shapes of QDRs. The calculated results are useful in designing and fabricating the interrelated photoelectric devices. The single electron states presented here are useful for the study of the electron correlations and the effects of magnetic fields in QDRs
Elliptic Calabi-Yau Threefolds with Z_3 x Z_3 Wilson Lines
A torus fibered Calabi-Yau threefold with first homotopy group Z_3 x Z_3 is
constructed as a free quotient of a fiber product of two dP_9 surfaces.
Calabi-Yau threefolds of this type admit Z_3 x Z_3 Wilson lines. In conjunction
with SU(4) holomorphic vector bundles, such vacua lead to anomaly free, three
generation models of particle physics with a right handed neutrino and a
U(1)_{B-L} gauge factor, in addition to the SU(3)_C x SU(2)_L x U(1)_Y standard
model gauge group. This factor helps to naturally suppress nucleon decay. The
moduli space and Dolbeault cohomology of the threefold is also discussed.Comment: 51 pages, 13 figures; v2: references adde
Development of an eight-band theory for quantum-dot heterostructures
We derive a nonsymmetrized 8-band effective-mass Hamiltonian for quantum-dot
heterostructures (QDHs) in Burt's envelope-function representation. The 8x8
radial Hamiltonian and the boundary conditions for the Schroedinger equation
are obtained for spherical QDHs. Boundary conditions for symmetrized and
nonsymmetrized radial Hamiltonians are compared with each other and with
connection rules that are commonly used to match the wave functions found from
the bulk kp Hamiltonians of two adjacent materials. Electron and hole energy
spectra in three spherical QDHs: HgS/CdS, InAs/GaAs, and GaAs/AlAs are
calculated as a function of the quantum dot radius within the approximate
symmetrized and exact nonsymmetrized 8x8 models. The parameters of dissymmetry
are shown to influence the energy levels and the wave functions of an electron
and a hole and, consequently, the energies of both intraband and interband
transitions.Comment: 36 pages, 10 figures, E-mail addresses: [email protected],
[email protected]
Interface electronic states and boundary conditions for envelope functions
The envelope-function method with generalized boundary conditions is applied
to the description of localized and resonant interface states. A complete set
of phenomenological conditions which restrict the form of connection rules for
envelope functions is derived using the Hermiticity and symmetry requirements.
Empirical coefficients in the connection rules play role of material parameters
which characterize an internal structure of every particular heterointerface.
As an illustration we present the derivation of the most general connection
rules for the one-band effective mass and 4-band Kane models. The conditions
for the existence of Tamm-like localized interface states are established. It
is shown that a nontrivial form of the connection rules can also result in the
formation of resonant states. The most transparent manifestation of such states
is the resonant tunneling through a single-barrier heterostructure.Comment: RevTeX4, 11 pages, 5 eps figures, submitted to Phys.Rev.
Electron and hole states in quantum-dot quantum wells within a spherical 8-band model
In order to study heterostructures composed both of materials with strongly
different parameters and of materials with narrow band gaps, we have developed
an approach, which combines the spherical 8-band effective-mass Hamiltonian and
the Burt's envelope function representation. Using this method, electron and
hole states are calculated in CdS/HgS/CdS/H_2O and CdTe/HgTe/CdTe/H_2O
quantum-dot quantum-well heterostructures. Radial components of the wave
functions of the lowest S and P electron and hole states in typical quantum-dot
quantum wells (QDQWs) are presented as a function of radius. The 6-band-hole
components of the radial wave functions of an electron in the 8-band model have
amplitudes comparable with the amplitude of the corresponding 2-band-electron
component. This is a consequence of the coupling between the conduction and
valence bands, which gives a strong nonparabolicity of the conduction band. At
the same time, the 2-band-electron component of the radial wave functions of a
hole in the 8-band model is small compared with the amplitudes of the
corresponding 6-band-hole components. It is shown that in the CdS/HgS/CdS/H_2O
QDQW holes in the lowest states are strongly localized in the well region
(HgS). On the contrary, electrons in this QDQW and both electron and holes in
the CdTe/HgTe/CdTe/H_2O QDQW are distributed through the entire dot. The
importance of the developed theory for QDQWs is proven by the fact that in
contrast to our rigorous 8-band model, there appear spurious states within the
commonly used symmetrized 8-band model.Comment: 15 pages, 5 figures, E-mail addresses: [email protected],
[email protected]
The Spectra of Heterotic Standard Model Vacua
A formalism for determining the massless spectrum of a class of realistic
heterotic string vacua is presented. These vacua, which consist of SU(5)
holomorphic bundles on torus-fibered Calabi-Yau threefolds with fundamental
group Z_2, lead to low energy theories with standard model gauge group (SU(3)_C
x SU(2)_L x U(1)_Y)/Z_6 and three families of quarks and leptons. A methodology
for determining the sheaf cohomology of these bundles and the representation of
Z_2 on each cohomology group is given. Combining these results with the action
of a Z_2 Wilson line, we compute, tabulate and discuss the massless spectrum.Comment: 41+1pp, 2 fig
The Particle Spectrum of Heterotic Compactifications
Techniques are presented for computing the cohomology of stable, holomorphic
vector bundles over elliptically fibered Calabi-Yau threefolds. These
cohomology groups explicitly determine the spectrum of the low energy,
four-dimensional theory. Generic points in vector bundle moduli space manifest
an identical spectrum. However, it is shown that on subsets of moduli space of
co-dimension one or higher, the spectrum can abruptly jump to many different
values. Both analytic and numerical data illustrating this phenomenon are
presented. This result opens the possibility of tunneling or phase transitions
between different particle spectra in the same heterotic compactification. In
the course of this discussion, a classification of SU(5) GUT theories within a
specific context is presented.Comment: 77 pages, 3 figure
Heterotic Standard Model Moduli
In previous papers, we introduced a heterotic standard model and discussed
its basic properties. The Calabi-Yau threefold has, generically, three Kahler
and three complex structure moduli. The observable sector of this vacuum has
the spectrum of the MSSM with one additional pair of Higgs-Higgs conjugate
fields. The hidden sector has no charged matter in the strongly coupled string
and only minimal matter for weak coupling. Additionally, the spectrum of both
sectors will contain vector bundle moduli. The exact number of such moduli was
conjectured to be small, but was not explicitly computed. In this paper, we
rectify this and present a formalism for computing the number of vector bundle
moduli. Using this formalism, the number of moduli in both the observable and
strongly coupled hidden sectors is explicitly calculated.Comment: 28 pages, LaTeX; v2: typos corrected, references added; v3:
clarifications, references adde
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