934 research outputs found
An SU(5) Heterotic Standard Model
We introduce a new heterotic Standard Model which has precisely the spectrum
of the Minimal Supersymmetric Standard Model (MSSM), with no exotic matter. The
observable sector has gauge group SU(3) x SU(2) x U(1). Our model is obtained
from a compactification of heterotic strings on a Calabi-Yau threefold with Z_2
fundamental group, coupled with an invariant SU(5) bundle. Depending on the
region of moduli space in which the model lies, we obtain a spectrum consisting
of the three generations of the Standard Model, augmented by 0, 1 or 2 Higgs
doublet conjugate pairs. In particular, we get the first compactification
involving a heterotic string vacuum (i.e. a {\it stable} bundle) yielding
precisely the MSSM with a single pair of Higgs.Comment: 15 page
Moduli Dependent Spectra of Heterotic Compactifications
Explicit methods are presented for computing the cohomology of stable,
holomorphic vector bundles on elliptically fibered Calabi-Yau threefolds. The
complete particle spectrum of the low-energy, four-dimensional theory is
specified by the dimensions of specific cohomology groups. The spectrum is
shown to depend on the choice of vector bundle moduli, jumping up from a
generic minimal result to attain many higher values on subspaces of
co-dimension one or higher in the moduli space. An explicit example is
presented within the context of a heterotic vacuum corresponding to an SU(5)
GUT in four-dimensions.Comment: 11+1 pages, 2 figures, comments adde
Higgs Doublets, Split Multiplets and Heterotic SU(3)_C x SU(2)_L x U(1)_Y Spectra
A methodology for computing the massless spectrum of heterotic vacua with
Wilson lines is presented. This is applied to a specific class of vacua with
holomorphic SU(5)-bundles over torus-fibered Calabi-Yau threefolds with
fundamental group Z_2. These vacua lead to low energy theories with the
standard model gauge group SU(3)_C x SU(2)_L x U(1)_Yand three families of
quark/leptons. The massless spectrum is computed, including the multiplicity of
Higgs doublets.Comment: 11+1 p
Invariant Homology on Standard Model Manifolds
Torus-fibered Calabi-Yau threefolds Z, with base dP_9 and fundamental group
pi_1(Z)=Z_2 X Z_2, are reviewed. It is shown that Z=X/(Z_2 X Z_2), where X=B
X_{P_1} B' are elliptically fibered Calabi-Yau threefolds that admit a freely
acting Z_2 X Z_2 automorphism group. B and B' are rational elliptic surfaces,
each with a Z_2 X Z_2 group of automorphisms. It is shown that the Z_2 X Z_2
invariant classes of curves of each surface have four generators which produce,
via the fiber product, seven Z_2 X Z_2 invariant generators in H_4(X,Z). All
invariant homology classes are computed explicitly. These descend to produce a
rank seven homology group H_4(Z,Z) on Z. The existence of these homology
classes on Z is essential to the construction of anomaly free, three family
standard-like models with suppressed nucleon decay in both weakly and strongly
coupled heterotic superstring theory.Comment: 57 pages, 13 figure
Torus-Fibered Calabi-Yau Threefolds with Non-Trivial Fundamental Group
We construct smooth Calabi-Yau threefolds Z, torus-fibered over a dP_9 base,
with fundamental group Z_2 X Z_2. To do this, the structure of rational
elliptic surfaces is studied and it is shown that a restricted subset of such
surfaces admit at least a Z_2 X Z_2 group of automorphisms. One then constructs
Calabi-Yau threefolds X as the fiber product of two such dP_9 surfaces,
demonstrating that the involutions on the surfaces lift to a freely acting Z_2
X Z_2 group of automorphisms on X. The threefolds Z are then obtained as the
quotient Z=X/(Z_2 X Z_2). These Calabi-Yau spaces Z admit stable, holomorphic
SU(4) vector bundles which, in conjunction with Z_2 X Z_2 Wilson lines, lead to
standard-like models of particle physics with naturally suppressed nucleon
decay.Comment: 60 pages, 13 figures, Typos correcte
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
SU(4) Instantons on Calabi-Yau Threefolds with Z_2 x Z_2 Fundamental Group
Structure group SU(4) gauge vacua of both weakly and strongly coupled
heterotic superstring theory compactified on torus-fibered Calabi-Yau
threefolds Z with Z_2 x Z_2 fundamental group are presented. This is
accomplished by constructing invariant, stable, holomorphic rank four vector
bundles on the simply connected cover of Z. Such bundles can descend either to
Hermite-Yang-Mills instantons on Z or to twisted gauge fields satisfying the
Hermite-Yang-Mills equation corrected by a non-trivial flat B-field. It is
shown that large families of such instantons satisfy the constraints imposed by
particle physics phenomenology. The discrete parameter spaces of those families
are presented, as well as a lower bound on the dimension of the continuous
moduli of any such vacuum. In conjunction with Z_2 x Z_2 Wilson lines, these
SU(4) gauge vacua can lead to standard-like models at low energy with an
additional U(1)_{B-L} symmetry. This U(1)_{B-L} symmetry is very helpful in
naturally suppressing nucleon decay.Comment: 68 pages, no figure
Moduli in N=1 heterotic/F-theory duality
The moduli in a 4D N=1 heterotic compactification on an elliptic CY, as well
as in the dual F-theoretic compactification, break into "base" parameters which
are even (under the natural involution of the elliptic curves), and "fiber" or
twisting parameters; the latter include a continuous part which is odd, as well
as a discrete part. We interpret all the heterotic moduli in terms of
cohomology groups of the spectral covers, and identify them with the
corresponding F-theoretic moduli in a certain stable degeneration. The argument
is based on the comparison of three geometric objects: the spectral and cameral
covers and the ADE del Pezzo fibrations. For the continuous part of the
twisting moduli, this amounts to an isomorphism between certain abelian
varieties: the connected component of the heterotic Prym variety (a modified
Jacobian) and the F-theoretic intermediate Jacobian. The comparison of the
discrete part generalizes the matching of heterotic 5brane / F-theoretic 3brane
impurities.Comment: Latex, 26 pages. Acknowledgements adde
Vector Bundle Moduli and Small Instanton Transitions
We give the general presciption for calculating the moduli of irreducible,
stable SU(n) holomorphic vector bundles with positive spectral covers over
elliptically fibered Calabi-Yau threefolds. Explicit results are presented for
Hirzebruch base surfaces B=F_r. The transition moduli that are produced by
chirality changing small instanton phase transitions are defined and
specifically enumerated. The origin of these moduli, as the deformations of the
spectral cover restricted to the ``lift'' of the horizontal curve of the
M5-brane, is discussed. We present an alternative description of the transition
moduli as the sections of rank n holomorphic vector bundles over the M5-brane
curve and give explicit examples. Vector bundle moduli appear as gauge singlet
scalar fields in the effective low-energy actions of heterotic superstrings and
heterotic M-theory.Comment: 52 pages, LATEX, corrected typo
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