14 research outputs found
Wilson lines and Chern-Simons flux in explicit heterotic Calabi-Yau compactifications
We study to what extent Wilson lines in heterotic Calabi-Yau
compactifications lead to non-trivial H-flux via Chern-Simons terms. Wilson
lines are basic ingredients for Standard Model constructions but their induced
H-flux may affect the consistency of the leading order background geometry and
of the two-dimensional worldsheet theory. Moreover H-flux in heterotic
compactifications would play an important role for moduli stabilization and
could strongly constrain the supersymmetry breaking scale. We show how to
compute H-flux and the corresponding superpotential, given an explicit complete
intersection Calabi-Yau compactification and choice of Wilson lines. We do so
by classifying special Lagrangian submanifolds in the Calabi-Yau, understanding
how the Wilson lines project onto these submanifolds, and computing their
Chern-Simons invariants. We illustrate our procedure with the quintic
hypersurface as well as the split-bicubic, which can provide a potentially
realistic three generation model.Comment: 41 pages, 7 figures. v2: Minor corrections, published versio
Injective and Projective Semimodules over Involutive Semirings
We show that the term equivalence between MV-algebras and MV-semirings lifts to involutive residuated lattices and a class of semirings called involutive semirings. The semiring perspective leads to a necessary and sufficient condition for the interval [d,1] to be a subalgebra of an involutive residuated lattice, where d is the dualizing element. We also import some results and techniques of semimodule theory in the study of this class of semirings, generalizing results about injective and projective MV-semimodules. Indeed, we note that the involution plays a crucial role and that the results for MV-semirings are still true for involutive semirings whenever the Mundici functor is not involved. In particular, we prove that involution is a necessary and sufficient condition in order for projective and injective semimodules to coincide
Towards Open String Mirror Symmetry for One-Parameter Calabi-Yau Hypersurfaces
This work is concerned with branes and differential equations for
one-parameter Calabi-Yau hypersurfaces in weighted projective spaces. For a
certain class of B-branes we derive the inhomogeneous Picard--Fuchs equations
satisfied by the brane superpotential. In this way we arrive at a prediction
for the real BPS invariants for holomorphic maps of worldsheets with low Euler
characteristics, ending on the mirror A-branes.Comment: 68+1 pages, 4 figures, v2: references added, typos correcte
On integrability of Hirota-Kimura type discretizations
We give an overview of the integrability of the Hirota-Kimura discretization
method applied to algebraically completely integrable (a.c.i.) systems with
quadratic vector fields. Along with the description of the basic mechanism of
integrability (Hirota-Kimura bases), we provide the reader with a fairly
complete list of the currently available results for concrete a.c.i. systems.Comment: 47 pages, some minor change