17 research outputs found
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
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
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
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
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
Non-linear Realizations of Conformal Symmetry and Effective Field Theory for the Pseudo-Conformal Universe
The pseudo-conformal scenario is an alternative to inflation in which the
early universe is described by an approximate conformal field theory on flat,
Minkowski space. Some fields acquire a time-dependent expectation value, which
breaks the flat space so(4,2) conformal algebra to its so(4,1) de Sitter
subalgebra. As a result, weight-0 fields acquire a scale invariant spectrum of
perturbations. The scenario is very general, and its essential features are
determined by the symmetry breaking pattern, irrespective of the details of the
underlying microphysics. In this paper, we apply the well-known coset technique
to derive the most general effective lagrangian describing the Goldstone field
and matter fields, consistent with the assumed symmetries. The resulting action
captures the low energy dynamics of any pseudo-conformal realization, including
the U(1)-invariant quartic model and the Galilean Genesis scenario. We also
derive this lagrangian using an alternative method of curvature invariants,
consisting of writing down geometric scalars in terms of the conformal mode.
Using this general effective action, we compute the two-point function for the
Goldstone and a fiducial weight-0 field, as well as some sample three-point
functions involving these fields.Comment: 49 pages. v2: minor corrections, added references. v3: minor edits,
version appearing in JCA
The Pseudo-Conformal Universe: Scale Invariance from Spontaneous Breaking of Conformal Symmetry
We present a novel theory of the very early universe which addresses the
traditional horizon and flatness problems of big bang cosmology and predicts a
scale invariant spectrum of perturbations. Unlike inflation, this scenario
requires no exponential accelerated expansion of space-time. Instead, the early
universe is described by a conformal field theory minimally coupled to gravity.
The conformal fields develop a time-dependent expectation value which breaks
the flat space so(4,2) conformal symmetry down to so(4,1), the symmetries of de
Sitter, giving perturbations a scale invariant spectrum. The solution is an
attractor, at least in the case of a single time-dependent field. Meanwhile,
the metric background remains approximately flat but slowly contracts, which
makes the universe increasingly flat, homogeneous and isotropic, akin to the
smoothing mechanism of ekpyrotic cosmology. Our scenario is very general,
requiring only a conformal field theory capable of developing the appropriate
time-dependent expectation values, and encompasses existing incarnations of
this idea, specifically the U(1) model of Rubakov and the Galileon Genesis
scenario. Its essential features depend only on the symmetry breaking pattern
and not on the details of the underlying lagrangian. It makes generic
observational predictions that make it potentially distinguishable from
standard inflation, in particular significant non-gaussianities and the absence
of primordial gravitational waves.Comment: 51 pages, 3 figures. v2 discussion and refs added, minus sign in
transformation laws fixed. Version appearing in JCA
Simple Dynamics on the Brane
We apply methods of dynamical systems to study the behaviour of the
Randall-Sundrum models. We determine evolutionary paths for all possible
initial conditions in a 2-dimensional phase space and we investigate the set of
accelerated models. The simplicity of our formulation in comparison to some
earlier studies is expressed in the following: our dynamical system is a
2-dimensional Hamiltonian system, and what is more advantageous, it is free
from the degeneracy of critical points so that the system is structurally
stable. The phase plane analysis of Randall-Sundrum models with isotropic
Friedmann geometry clearly shows that qualitatively we deal with the same types
of evolution as in general relativity, although quantitatively there are
important differences.Comment: an improved version, 34 pages, 9 eps figure
Global Fluctuation Spectra in Big Crunch/Big Bang String Vacua
We study Big Crunch/Big Bang cosmologies that correspond to exact world-sheet
superconformal field theories of type II strings. The string theory spacetime
contains a Big Crunch and a Big Bang cosmology, as well as additional
``whisker'' asymptotic and intermediate regions. Within the context of free
string theory, we compute, unambiguously, the scalar fluctuation spectrum in
all regions of spacetime. Generically, the Big Crunch fluctuation spectrum is
altered while passing through the bounce singularity. The change in the
spectrum is characterized by a function , which is momentum and
time-dependent. We compute explicitly and demonstrate that it arises
from the whisker regions. The whiskers are also shown to lead to
``entanglement'' entropy in the Big Bang region. Finally, in the Milne orbifold
limit of our superconformal vacua, we show that and, hence, the
fluctuation spectrum is unaltered by the Big Crunch/Big Bang singularity. We
comment on, but do not attempt to resolve, subtleties related to gravitational
backreaction and light winding modes when interactions are taken into account.Comment: 68 pages, 1 figure; typos correcte
Primordial perturbations in a non singular bouncing universe model
We construct a simple non singular cosmological model in which the currently
observed expansion phase was preceded by a contraction. This is achieved, in
the framework of pure general relativity, by means of a radiation fluid and a
free scalar field having negative energy. We calculate the power spectrum of
the scalar perturbations that are produced in such a bouncing model and find
that, under the assumption of initial vacuum state for the quantum field
associated with the hydrodynamical perturbation, this leads to a spectral index
n=-1. The matching conditions applying to this bouncing model are derived and
shown to be different from those in the case of a sharp transition. We find
that if our bounce transition can be smoothly connected to a slowly contracting
phase, then the resulting power spectrum will be scale invariant.Comment: 11 pages, RevTeX 4, 8 figures, submitted to Phys. Rev.