5,984 research outputs found
Gauge Five Brane Dynamics And Small Instanton Transitions In Heterotic Models
We present the first examples of cosmological solutions to four-dimensional
heterotic models which include an evolving bundle modulus. The particular
bundle modulus we consider corresponds to the width of a gauge five brane. As
such our solutions can be used to describe the evolution in one of these models
after a small instanton transition. We find that certain properties are generic
to these solutions, regardless of initial conditions. This enables us to make
some definite statements about the dynamics subsequent to a small instanton
transition despite the fact that we cannot microscopically describe the process
itself. We also show that an effective description of the small instanton
transition by a continuous matching of fields and their first derivatives is
precluded by the form of the respective low-energy theories before and after
the transition.Comment: 16 pages, 3 figure
A Heterotic Standard Model with B-L Symmetry and a Stable Proton
We consider heterotic Calabi-Yau compactifications with S(U(4)xU(1))
background gauge fields. These models lead to gauge groups with an additional
U(1) factor which, under certain conditions, can combine with hypercharge to a
B-L symmetry. The associated gauge boson is automatically super-massive and,
hence, does not constitute a phenomenological problem. We illustrate this class
of compactifications with a model based on the monad construction, which leads
to a supersymmetric standard model with three families of quarks and leptons,
one pair of Higgs doublets, three right-handed neutrinos and no exotics charged
under the standard model group. The presence of the B-L symmetry means that the
model is safe from proton decay induced by dimension four operators. Due to the
presence of a special locus in moduli space where the bundle structure group is
Abelian and the low-energy symmetry enhances we can also show the absence of
dimension five proton-decay inducing operators.Comment: 23 pages Late
Non-generic Couplings in Supersymmetric Standard Models
We study two phases of a heterotic standard model, obtained from a Calabi-Yau
compactification of the E8xE8 heterotic string, in the context of the
associated four-dimensional effective theories. In the first phase we have a
standard model gauge group, an MSSM spectrum, four additional U(1) symmetries
and singlet fields. In the second phase, obtained from the first by continuing
along the singlet directions, three of the additional U(1) symmetries are
spontaneously broken and the remaining one is a B-L symmetry. In this second
phase, dimension five operators inducing proton decay are consistent with all
symmetries and as such, they are expected to be present. We show that, contrary
to this expectation, these operators are forbidden due to the additional U(1)
symmetries present in the first phase of the model. We emphasize that such
'unexpected' absences of operators, due to symmetry enhancement at specific
loci in the moduli space, can be phenomenologically relevant and, in the
present case, protect the model from fast proton decay.Comment: 5 page
Holomorphic Yukawa Couplings for Complete Intersection Calabi-Yau Manifolds
We develop methods to compute holomorphic Yukawa couplings for heterotic
compactifications on complete intersection Calabi-Yau manifolds, generalising
results of an earlier paper for Calabi-Yau hypersurfaces. Our methods are based
on constructing the required bundle-valued forms explicitly and evaluating the
relevant integrals over the projective ambient space. We also show how our
approach relates to an earlier, algebraic one to calculate the holomorphic
Yukawa couplings. A vanishing theorem, which we prove, implies that certain
Yukawa couplings allowed by low-energy symmetries are zero due to topological
reasons. To illustrate our methods, we calculate Yukawa couplings for
SU(5)-based standard models on a co-dimension two complete intersection
manifold.Comment: 40 pages, Latex; v2: minor corrections, references adde
A Variational Perspective on Accelerated Methods in Optimization
Accelerated gradient methods play a central role in optimization, achieving
optimal rates in many settings. While many generalizations and extensions of
Nesterov's original acceleration method have been proposed, it is not yet clear
what is the natural scope of the acceleration concept. In this paper, we study
accelerated methods from a continuous-time perspective. We show that there is a
Lagrangian functional that we call the \emph{Bregman Lagrangian} which
generates a large class of accelerated methods in continuous time, including
(but not limited to) accelerated gradient descent, its non-Euclidean extension,
and accelerated higher-order gradient methods. We show that the continuous-time
limit of all of these methods correspond to traveling the same curve in
spacetime at different speeds. From this perspective, Nesterov's technique and
many of its generalizations can be viewed as a systematic way to go from the
continuous-time curves generated by the Bregman Lagrangian to a family of
discrete-time accelerated algorithms.Comment: 38 pages. Subsumes an earlier working draft arXiv:1509.0361
Guaranteed Convergence of a Regularized Kohn-Sham Iteration in Finite Dimensions
The exact Kohn-Sham iteration of generalized density-functional theory in
finite dimensions witha Moreau-Yosida regularized universal Lieb functional and
an adaptive damping step is shown toconverge to the correct ground-state
density.Comment: 3 figures, contains erratum with additional author Paul E. Lammer
Making Distinct Dynamical Systems Appear Spectrally Identical
We show that a laser pulse can always be found that induces a desired optical
response from an arbitrary dynamical system. As illustrations, driving fields
are computed to induce the same optical response from a variety of distinct
systems (open and closed, quantum and classical). As a result, the observed
induced dipolar spectra without detailed information on the driving field is
not sufficient to characterize atomic and molecular systems. The formulation
may also be applied to design materials with specified optical characteristics.
These findings reveal unexplored flexibilities of nonlinear optics.Comment: 9 pages, 5 figure
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