216 research outputs found
A Non-Perturbative Superpotential With Symmetry
We compute the non-perturbative superpotential in -theory compactification
to four dimensions on a complex three-fold , where is a
rational elliptic surface. In contrast to examples considered previously, the
superpotential in this case has interesting modular properties; it is
essentially an theta function.Comment: Additional references and clarifications. Latex, 10 page
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
Vector Bundle Moduli Superpotentials in Heterotic Superstrings and M-Theory
The non-perturbative superpotential generated by a heterotic superstring
wrapped once around a genus-zero holomorphic curve is proportional to the
Pfaffian involving the determinant of a Dirac operator on this curve. We show
that the space of zero modes of this Dirac operator is the kernel of a linear
mapping that is dependent on the associated vector bundle moduli. By explicitly
computing the determinant of this map, one can deduce whether or not the
dimension of the space of zero modes vanishes. It is shown that this
information is sufficient to completely determine the Pfaffian and, hence, the
non-perturbative superpotential as explicit holomorphic functions of the vector
bundle moduli. This method is illustrated by a number of non-trivial examples.Comment: 81 pages, LaTeX, corrected typo
The Dynamics of Small Instanton Phase Transitions
The small instanton transition of a five-brane colliding with one end of the
S1/Z2 interval in heterotic M-theory is discussed, with emphasis on the
transition moduli, their potential function and the associated non-perturbative
superpotential. Using numerical methods, the equations of motion of these
moduli coupled to an expanding Friedmann-Robertson-Walker spacetime are solved
including non-perturbative interactions. It is shown that the five-brane
collides with the end of the interval at a small instanton. However, the moduli
then continue to evolve to an isolated minimum of the potential, where they are
trapped by gravitational damping. The torsion free sheaf at the small instanton
is ``smoothed out'' into a vector bundle at the isolated minimum, thus
dynamically completing the small instanton phase transition. Radiative damping
at the origin of moduli space is discussed and shown to be insufficient to trap
the moduli at the small instanton point.Comment: LaTeX, 23 pages, 7 figures; minor corrections, references 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
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
SU(5) Heterotic Standard Model Bundles
We construct a class of stable SU(5) bundles on an elliptically fibered
Calabi-Yau threefold with two sections, a variant of the ordinary Weierstrass
fibration, which admits a free involution. The bundles are invariant under the
involution, solve the topological constraint imposed by the heterotic anomaly
equation and give three generations of Standard Model fermions after symmetry
breaking by Wilson lines of the intermediate SU(5) GUT-group to the Standard
Model gauge group. Among the solutions we find some which can be perturbed to
solutions of the Strominger system. Thus these solutions provide a step toward
the construction of phenomenologically realistic heterotic flux
compactifications via non-Kahler deformations of Calabi-Yau geometries with
bundles. This particular class of solutions involves a rank two hidden sector
bundle and does not require background fivebranes for anomaly cancellation.Comment: 17 page
Geometric transitions and integrable systems
We consider {\bf B}-model large duality for a new class of noncompact
Calabi-Yau spaces modeled on the neighborhood of a ruled surface in a
Calabi-Yau threefold. The closed string side of the transition is governed at
genus zero by an Hitchin integrable system on a genus Riemann surface
. The open string side is described by a holomorphic Chern-Simons
theory which reduces to a generalized matrix model in which the eigenvalues lie
on the compact Riemann surface . We show that the large planar
limit of the generalized matrix model is governed by the same Hitchin
system therefore proving genus zero large duality for this class of
transitions.Comment: 70 pages, 1 figure; version two: minor change
Vacuum Stability in Heterotic M-Theory
The problem of the stabilization of moduli is discussed within the context of
compactified strongly coupled heterotic string theory. It is shown that all
geometric, vector bundle and five-brane moduli are completely fixed, within a
phenomenologically acceptable range, by non-perturbative physics. This result
requires, in addition to the full space of moduli, non-vanishing Neveu-Schwarz
flux, gaugino condensation with threshold corrections and the explicit form of
the Pfaffians in string instanton superpotentials. The stable vacuum presented
here has a negative cosmological constant. The possibility of ``lifting'' this
to a metastable vacuum with positive cosmological constant is briefly
discussed.Comment: 39 pages, minor correction
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