5,835 research outputs found
Notes on Certain (0,2) Correlation Functions
In this paper we shall describe some correlation function computations in
perturbative heterotic strings that, for example, in certain circumstances can
lend themselves to a heterotic generalization of quantum cohomology
calculations. Ordinary quantum chiral rings reflect worldsheet instanton
corrections to correlation functions involving products of Dolbeault cohomology
groups on the target space. The heterotic generalization described here
involves computing worldsheet instanton corrections to correlation functions
defined by products of elements of sheaf cohomology groups. One must not only
compactify moduli spaces of rational curves, but also extend a sheaf
(determined by the gauge bundle) over the compactification, and linear sigma
models provide natural mechanisms for doing both. Euler classes of obstruction
bundles generalize to this language in an interesting way.Comment: 51 pages, LaTeX; v2: typos fixed; v3: more typos fixe
Cohomology of Line Bundles: A Computational Algorithm
We present an algorithm for computing line bundle valued cohomology classes
over toric varieties. This is the basic starting point for computing massless
modes in both heterotic and Type IIB/F-theory compactifications, where the
manifolds of interest are complete intersections of hypersurfaces in toric
varieties supporting additional vector bundles.Comment: 11 pages, 1 figure, 2 tables; v2: typos and references corrected; v3:
proof-related statements updated, cohomCalg implementation available at
http://wwwth.mppmu.mpg.de/members/blumenha/cohomcalg
Yang-Mills Chern-Simons Corrections From the Pure Spinor Superstring
Nilpotency of the pure spinor BRST operator in a curved background implies
superspace equations of motion for the background. By computing one-loop
corrections to nilpotency for the heterotic sigma model, the Yang-Mills
Chern-Simons corrections to the background are derived.Comment: 25 pages, harvmac tex, 15 diagrams; references adde
Yukawa Couplings in Heterotic Standard Models
In this paper, we present a formalism for computing the Yukawa couplings in
heterotic standard models. This is accomplished by calculating the relevant
triple products of cohomology groups, leading to terms proportional to Q*H*u,
Q*Hbar*d, L*H*nu and L*Hbar*e in the low energy superpotential. These
interactions are subject to two very restrictive selection rules arising from
the geometry of the Calabi-Yau manifold. We apply our formalism to the
"minimal" heterotic standard model whose observable sector matter spectrum is
exactly that of the MSSM. The non-vanishing Yukawa interactions are explicitly
computed in this context. These interactions exhibit a texture rendering one
out of the three quark/lepton families naturally light.Comment: 21 pages, LaTe
Moduli Dependent mu-Terms in a Heterotic Standard Model
In this paper, we present a formalism for computing the non-vanishing Higgs
mu-terms in a heterotic standard model. This is accomplished by calculating the
cubic product of the cohomology groups associated with the vector bundle moduli
(phi), Higgs (H) and Higgs conjugate (Hbar) superfields. This leads to terms
proportional to phi H Hbar in the low energy superpotential which, for non-zero
moduli expectation values, generate moduli dependent mu-terms of the form
H Hbar. It is found that these interactions are subject to two very restrictive
selection rules, each arising from a Leray spectral sequence, which greatly
reduce the number of moduli that can couple to Higgs-Higgs conjugate fields. We
apply our formalism to a specific heterotic standard model vacuum. The
non-vanishing cubic interactions phi H Hbar are explicitly computed in this
context and shown to contain only four of the nineteen vector bundle moduli.Comment: 23 pages, LaTe
Towards heterotic computing with droplets in a fully automated droplet-maker platform
The control and prediction of complex chemical systems is a difficult problem due to the nature of the interactions, transformations and processes occurring. From self-assembly to catalysis and self-organization, complex chemical systems are often heterogeneous mixtures that at the most extreme exhibit system-level functions, such as those that could be observed in a living cell. In this paper, we outline an approach to understand and explore complex chemical systems using an automated droplet maker to control the composition, size and position of the droplets in a predefined chemical environment. By investigating the spatio-temporal dynamics of the droplets, the aim is to understand how to control system-level emergence of complex chemical behaviour and even view the system-level behaviour as a programmable entity capable of information processing. Herein, we explore how our automated droplet-maker platform could be viewed as a prototype chemical heterotic computer with some initial data and example problems that may be viewed as potential chemically embodied computations
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