19 research outputs found
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
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
Numerical solution to the hermitian Yang-Mills equation on the Fermat quintic
We develop an iterative method for finding solutions to the hermitian
Yang-Mills equation on stable holomorphic vector bundles, following ideas
recently developed by Donaldson. As illustrations, we construct numerically the
hermitian Einstein metrics on the tangent bundle and a rank three vector bundle
on P^2. In addition, we find a hermitian Yang-Mills connection on a stable rank
three vector bundle on the Fermat quintic.Comment: 25 pages, 2 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
Numerical Calabi-Yau metrics
We develop numerical methods for approximating Ricci flat metrics on
Calabi-Yau hypersurfaces in projective spaces. Our approach is based on finding
balanced metrics, and builds on recent theoretical work by Donaldson. We
illustrate our methods in detail for a one parameter family of quintics. We
also suggest several ways to extend our results.Comment: 23 pages, 3 figure
Non-Perturbative Superpotentials from Membrane Instantons in Heterotic M-Theory
A formalism for calculating the open supermembrane contribution to the
non-perturbative superpotential of moduli in heterotic M-theory is presented.
This is explicitly applied to the Calabi-Yau (1,1)-moduli and the separation
modulus of the end-of-the-world BPS three-branes, whose non-perturbative
superpotential is computed. The role of gauge bundles on the boundaries of the
open supermembranes is discussed in detail, and a topological criterion
presented for the associated superpotential to be non-vanishing.Comment: 59 pages, latex, minor corrections adde
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
Massless Spectra of Three Generation U(N) Heterotic String Vacua
We provide the methods to compute the complete massless spectra of a class of
recently introduced supersymmetric E8 x E8 heterotic string models which invoke
vector bundles with U(N) structure group on simply connected Calabi-Yau
manifolds and which yield flipped SU(5) and MSSM string vacua of potential
phenomenological interest. We apply Leray spectral sequences in order to derive
the localisation of the cohomology groups H^i(X,V_a \times V_b),
H^i(X,\bigwedge^2 V) and H^i(X,{\bf S}^2 V) for vector bundles defined via
Fourier-Mukai transforms on elliptically fibered Calabi-Yau manifolds. By the
method of bundle extensions we define a stable U(4) vector bundle leading to
the first flipped SU(5) model with just three generations, i.e. without any
vector-like matter. Along the way, we propose the notion of Lambda-stability
for heterotic bundles.Comment: 48 page