19 research outputs found
Vertex algebras and the Landau-Ginzburg/Calabi-Yau correspondence
We construct a spectral sequence that converges to the cohomology of the
chiral de Rham complex over a Calabi-Yau hypersurface and whose first term is a
vertex algebra closely related to the Landau-Ginburg orbifold. As an
application, we prove an explicit orbifold formula for the elliptic genus of
Calabi-Yau hypersurfaces.Comment: Latex, 50p. Some typos corrected, the page size may have been fixed.
One new result, a theorem on the vertx algebra structure of the
Landau-Ginzburg orbifold appears in sect. 5.2.18. This is the final version
to appear in the Moscow Mathematical Journa
Multiloop Superstring Amplitudes from Non-Minimal Pure Spinor Formalism
Using the non-minimal version of the pure spinor formalism, manifestly
super-Poincare covariant superstring scattering amplitudes can be computed as
in topological string theory without the need of picture-changing operators.
The only subtlety comes from regularizing the functional integral over the pure
spinor ghosts. In this paper, it is shown how to regularize this functional
integral in a BRST-invariant manner, allowing the computation of arbitrary
multiloop amplitudes. The regularization method simplifies for scattering
amplitudes which contribute to ten-dimensional F-terms, i.e. terms in the
ten-dimensional superspace action which do not involve integration over the
maximum number of 's.Comment: 23 pages harvmac, added acknowledgemen
Two-Dimensional Twisted Sigma Models, the Mirror Chiral de Rham Complex, and Twisted Generalised Mirror Symmetry
In this paper, we study the perturbative aspects of a "B-twisted"
two-dimensional heterotic sigma model on a holomorphic gauge bundle
over a complex, hermitian manifold . We show that the model can
be naturally described in terms of the mathematical theory of ``Chiral
Differential Operators". In particular, the physical anomalies of the sigma
model can be reinterpreted as an obstruction to a global definition of the
associated sheaf of vertex superalgebras derived from the free conformal field
theory describing the model locally on . In addition, one can also obtain a
novel understanding of the sigma model one-loop beta function solely in terms
of holomorphic data. At the locus, one can describe the resulting
half-twisted variant of the topological B-model in terms of a
"Chiral de Rham complex" (or CDR) defined by Malikov et al. in \cite{GMS1}. Via
mirror symmetry, one can also derive various conjectural expressions relating
the sheaf cohomology of the mirror CDR to that of the original CDR on pairs of
Calabi-Yau mirror manifolds. An analysis of the half-twisted model on a
non-K\"ahler group manifold with torsion also allows one to draw conclusions
about the corresponding sheaves of CDR (and its mirror) that are consistent
with mathematically established results by Ben-Bassat in \cite{ben} on the
mirror symmetry of generalised complex manifolds. These conclusions therefore
suggest an interesting relevance of the sheaf of CDR in the recent study of
generalised mirror symmetry.Comment: 97 pages. Companion paper to hep-th/0604179. Published versio
Gepner-like models and Landau-Ginzburg/sigma-model correspondence
The Gepner-like models of -type is considered. When is multiple
of the elliptic genus and the Euler characteristic is calculated. Using
free-field representation we relate these models with -models on
hypersurfaces in the total space of anticanonical bundle over the projective
space
A heterotic sigma model with novel target geometry
We construct a (1,2) heterotic sigma model whose target space geometry
consists of a transitive Lie algebroid with complex structure on a Kaehler
manifold. We show that, under certain geometrical and topological conditions,
there are two distinguished topological half--twists of the heterotic sigma
model leading to A and B type half--topological models. Each of these models is
characterized by the usual topological BRST operator, stemming from the
heterotic (0,2) supersymmetry, and a second BRST operator anticommuting with
the former, originating from the (1,0) supersymmetry. These BRST operators
combined in a certain way provide each half--topological model with two
inequivalent BRST structures and, correspondingly, two distinct perturbative
chiral algebras and chiral rings. The latter are studied in detail and
characterized geometrically in terms of Lie algebroid cohomology in the
quasiclassical limit.Comment: 83 pages, no figures, 2 references adde
Chiral de Rham complex on Riemannian manifolds and special holonomy
Interpreting the chiral de Rham complex (CDR) as a formal Hamiltonian
quantization of the supersymmetric non-linear sigma model, we suggest a setup
for the study of CDR on manifolds with special holonomy. We show how to
systematically construct global sections of CDR from differential forms, and
investigate the algebra of the sections corresponding to the covariantly
constant forms associated with the special holonomy. As a concrete example, we
construct two commuting copies of the Odake algebra (an extension of the N=2
superconformal algebra) on the space of global sections of CDR of a Calabi-Yau
threefold and conjecture similar results for G_2 manifolds. We also discuss
quasi-classical limits of these algebras.Comment: 49 pages, title changed, major rewrite with no changes in the main
theorems, published versio
Beta-gamma systems and the deformations of the BRST operator
We describe the relation between simple logarithmic CFTs associated with
closed and open strings, and their "infinite metric" limits, corresponding to
the beta-gamma systems. This relation is studied on the level of the BRST
complex: we show that the consideration of metric as a perturbation leads to a
certain deformation of the algebraic operations of the Lian-Zuckerman type on
the vertex algebra, associated with the beta-gamma systems. The Maurer-Cartan
equations corresponding to this deformed structure in the quasiclassical
approximation lead to the nonlinear field equations. As an explicit example, we
demonstrate, that using this construction, Yang-Mills equations can be derived.
This gives rise to a nontrivial relation between the Courant-Dorfman algebroid
and homotopy algebras emerging from the gauge theory. We also discuss possible
algebraic approach to the study of beta-functions in sigma-models.Comment: LaTeX2e, 15 pages; minor revision, typos corrected, Journal of
Physics A, in pres