4,012 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

### Quantum cohomology of the cotangent bundle of a flag variety as a Yangian Bethe algebra

We interpret the equivariant cohomology algebra
H^*_{GL_n\times\C^*}(T^*F_\lambda;\C) of the cotangent bundle of a partial flag
variety F_\lambda parametrizing chains of subspaces 0=F_0\subset
F_1\subset\dots\subset F_N =\C^n, \dim F_i/F_{i-1}=\lambda_i, as the Yangian
Bethe algebra of the gl_N-weight subspace of a gl_N Yangian module. Under this
identification the dynamical connection of [TV1] turns into the quantum
connection of [BMO] and [MO]. As a result of this identification we describe
the algebra of quantum multiplication on H^*_{GL_n\times\C^*}(T^*F_\lambda;\C)
as the algebra of functions on fibers of a discrete Wronski map. In particular
this gives generators and relations of that algebra. This identification also
gives us hypergeometric solutions of the associated quantum differential
equation. That fact manifests the Landau-Ginzburg mirror symmetry for the
cotangent bundle of the flag variety.Comment: Latex, 45 pages, references added, Conjecture 7.10 is now Theorem
7.10, Theorem 7.13 adde

### BRST Operator for Quantum Lie Algebras: Relation to Bar Complex

Quantum Lie algebras (an important class of quadratic algebras arising in the
Woronowicz calculus on quantum groups) are generalizations of Lie (super)
algebras. Many notions from the theory of Lie (super)algebras admit ``quantum''
generalizations. In particular, there is a BRST operator Q (Q^2=0) which
generates the differential in the Woronowicz theory and gives information about
(co)homologies of quantum Lie algebras. In our previous papers a recurrence
relation for the operator Q for quantum Lie algebras was given and solved. Here
we consider the bar complex for q-Lie algebras and its subcomplex of
q-antisymmetric chains. We establish a chain map (which is an isomorphism) of
the standard complex for a q-Lie algebra to the subcomplex of the antisymmetric
chains. The construction requires a set of nontrivial identities in the group
algebra of the braid group. We discuss also a generalization of the standard
complex to the case when a q-Lie algebra is equipped with a grading operator.Comment: 20 page

### 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 $\theta$'s.Comment: 23 pages harvmac, added acknowledgemen

### Homological Algebra and Divergent Series

We study some features of infinite resolutions of Koszul algebras motivated by the developments in the string theory initiated by Berkovits

### Quantum cohomology of the cotangent bundle of a flag variety as a Yangian Bethe algebra

We interpret the equivariant cohomology algebra H∗GLn×C*(T*Fλ;C) of the cotangent bundle of a partial flag variety Fλ parametrizing chains of subspaces 0 = F0 ⊂ F1 ⊂ · · · ⊂ FN = Cn, dim Fi/Fi−1 = λi, as the Yangian Bethe algebra B∞( 1DV−λ) of the glN-weight subspace 1/DV−λ of a Y (glN)-module 1/DV−. Under this identification the dynamical connection of [TV1] turns into the quantum connection of [BMO] and [MO]. As a result of this identification we describe the algebra of quantum multiplication on H∗GLn×C*(T ∗Fλ;C) as the algebra of functions on fibers of a discrete Wronski map. In particular this gives generators and relations of that algebra. This identification also gives us hypergeometric solutions of the associated quantum differential equation. That fact manifests the Landau-Ginzburg mirror symmetry for the cotangent bundle of the flag variety

### 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 $(0,2)$ heterotic sigma model on a holomorphic gauge bundle
$\mathcal E$ over a complex, hermitian manifold $X$. 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 $X$. 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 $(2,2)$ locus, one can describe the resulting
half-twisted variant of the topological B-model in terms of a $\it{mirror}$
"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

### 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

### Fully Integrated Glass Microfluidic Device for Performing High-Efficiency Capillary Electrophoresis and Electrospray Ionization Mass Spectrometry

A microfabricated device has been developed in which electrospray ionization is performed directly from the corner of a rectangular glass microchip. The device allows highly efficient electrokinetically driven separations to be coupled directly to a mass spectrometer (MS) without the use of external pressure sources or the insertion of capillary spray tips. An electrokinetic-based hydraulic pump is integrated on the chip that directs eluting materials to the monolithically integrated spray tip. A positively charged surface coating, PolyE-323, is used to prevent surface interactions with peptides and proteins and to reverse the electroosmotic flow in the separation channel. The device has been used to perform microchip CE-MS analysis of peptides and proteins with efficiencies over 200 000 theoretical plates (1 000 000 plates/m). The sensitivity and stability of the microfabricated ESI source were found to be comparable to that of commercial pulled fused-silica capillary nanospray sources

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