68 research outputs found
Old issues and linear sigma models
Using mirror symmetry, we resolve an old puzzle in the linear sigma model
description of the spacetime Higgs mechanism in a heterotic string
compactification with (2,2) worldsheet supersymmetry. The resolution has a nice
spacetime interpretation via the normalization of physical fields and suggests
that with a little care deformations of the linear sigma model can describe
heterotic Higgs branches.Comment: 31 pages, xy-pic diagrams; v2: some additional comments, typos
corrected, improved discussion in appendix; v3: atmp forma
Small Landau-Ginzburg theories
We classify (0,2) Landau-Ginzburg theories that can flow to compact IR fixed
points with equal left and right central charges strictly bounded by 3. Our
result is a (0,2) generalization of the ADE classification of (2,2)
Landau-Ginzburg theories that flow to N=2 minimal models. Unitarity requires
the right-moving supersymmetric sector to fall into the standard N=2 minimal
model representations, but the left-moving sector need not have supersymmetry.
The Landau-Ginzburg realizations provide a simple way to compute the chiral
algebra and other characteristics of these fixed points. While our results
pertain to isolated superconformal theories, tensor products lead to (0,2)
superconformal theories with higher central charge, and the Landau-Ginzburg
realization provides a model for a class of marginal and relevant deformations
of such theories.Comment: 22 pages; typos fixed, added discussion on chiral algebr
(0,2) Landau-Ginzburg Models and Residues
We study the topological heterotic ring in (0,2) Landau-Ginzburg models
without a (2,2) locus. The ring elements correspond to elements of the Koszul
cohomology groups associated to a zero-dimensional ideal in a polynomial ring,
and the computation of half-twisted genus zero correlators reduces to a map
from the first non-trivial Koszul cohomology group to complex numbers. This map
is a generalization of the local Grothendieck residue. The results may be
applied to computations of Yukawa couplings in a heterotic compactification at
a Landau-Ginzburg point.Comment: 25 pages; typos fixed; published versio
Landau-Ginzburg skeletons
We study the class of indecomposable two-dimensional Landau-Ginzburg theories
with (2,2) supersymmetry and central charge c < 6 with the aim of classifying
all such theories up to marginal deformations. Our results include cases
overlooked in previous classifications. The results are rigorous for three or
fewer fields and more generally are rigorous if we assume an extra bound.
Numerics suggest that we have the complete set of indecomposable
Landau-Ginzburg families with c<6. This set consists of 38 infinite families
and a finite list of 418 sporadic cases. The basic tools are classic results of
Kreuzer and Skarke on quasi-homogeneous isolated singularities and solutions to
certain feasibility integer programming problems.Comment: 39 pages and tikz figures, three text files with LG charges included
in submission; v2 fixes two sets of charge
Recent Developments in (0,2) Mirror Symmetry
Mirror symmetry of the type II string has a beautiful generalization to the
heterotic string. This generalization, known as (0,2) mirror symmetry, is a
field still largely in its infancy. We describe recent developments including
the ideas behind quantum sheaf cohomology, the mirror map for deformations of
(2,2) mirrors, the construction of mirror pairs from worldsheet duality, as
well as an overview of some of the many open questions. The (0,2) mirrors of
Hirzebruch surfaces are presented as a new example
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