An Alternative Topological Field Theory of Generalized Complex Geometry

We propose a new topological field theory on generalized complex geometry in two dimension using AKSZ formulation. Zucchini's model is $A$ model in the case that the generalized complex structuredepends on only a symplectic structure. Our new model is $B$ model in the case that the generalized complex structure depends on only a complex structure.Comment: 29 pages, typos and references correcte

Toda Fields on Riemann Surfaces: remarks on the Miura transformation

We point out that the Miura transformation is related to a holomorphic foliation in a relative flag manifold over a Riemann Surface. Certain differential operators corresponding to a free field description of $W$--algebras are thus interpreted as partial connections associated to the foliation.Comment: AmsLatex 1.1, 10 page

Deformation Theory of Holomorphic Vector Bundles, Extended Conformal Symmetry and Extensions of 2D Gravity

Developing on the ideas of R. Stora and coworkers, a formulation of two dimensional field theory endowed with extended conformal symmetry is given, which is based on deformation theory of holomorphic and Hermitian spaces. The geometric background consists of a vector bundle $E$ over a closed surface $\Sigma$ endowed with a holomorphic structure and a Hermitian structure subordinated to it. The symmetry group is the semidirect product of the automorphism group ${\rm Aut}(E)$ of $E$ and the extended Weyl group ${\rm Weyl}(E)$ of $E$ and acts on the holomorphic and Hermitian structures. The extended Weyl anomaly can be shifted into an automorphism chirally split anomaly by adding to the action a local counterterm, as in ordinary conformal field theory. The dependence on the scale of the metric on the fiber of $E$ is encoded in the Donaldson action, a vector bundle generalization of the Liouville action. The Weyl and automorphism anomaly split into two contributions corresponding respectively to the determinant and projectivization of $E$. The determinant part induces an effective ordinary Weyl or diffeomorphism anomaly and the induced central charge can be computed.Comment: 49 pages, plain TeX. A number of misprints have been correcte

Generalized Kahler Geometry from supersymmetric sigma models

We give a physical derivation of generalized Kahler geometry. Starting from a supersymmetric nonlinear sigma model, we rederive and explain the results of Gualtieri regarding the equivalence between generalized Kahler geometry and the bi-hermitean geometry of Gates-Hull-Rocek. When cast in the language of supersymmetric sigma models, this relation maps precisely to that between the Lagrangian and the Hamiltonian formalisms. We also discuss topological twist in this context.Comment: 18 page

Induced Polyakov supergravity on Riemann surfaces of higher genus

An effective action is obtained for the $N=1$, $2D-$induced supergravity on a compact super Riemann surface (without boundary) $\hat\Sigma$ of genus $g>1$, as the general solution of the corresponding superconformal Ward identity. This is accomplished by defining a new super integration theory on $\hat\Sigma$ which includes a new formulation of the super Stokes theorem and residue calculus in the superfield formalism. Another crucial ingredient is the notion of polydromic fields. The resulting action is shown to be well-defined and free of singularities on \sig. As a by-product, we point out a morphism between the diffeomorphism symmetry and holomorphic properties.Comment: LPTB 93-10, Latex file 20 page

Poisson sigma model on the sphere

We evaluate the path integral of the Poisson sigma model on sphere and study the correlators of quantum observables. We argue that for the path integral to be well-defined the corresponding Poisson structure should be unimodular. The construction of the finite dimensional BV theory is presented and we argue that it is responsible for the leading semiclassical contribution. For a (twisted) generalized Kahler manifold we discuss the gauge fixed action for the Poisson sigma model. Using the localization we prove that for the holomorphic Poisson structure the semiclassical result for the correlators is indeed the full quantum result.Comment: 38 page

M-theory on eight-manifolds revisited: N=1 supersymmetry and generalized Spin(7) structures

The requirement of ${\cal N}=1$ supersymmetry for M-theory backgrounds of the form of a warped product ${\cal M}\times_{w}X$, where $X$ is an eight-manifold and ${\cal M}$ is three-dimensional Minkowski or AdS space, implies the existence of a nowhere-vanishing Majorana spinor $\xi$ on $X$. $\xi$ lifts to a nowhere-vanishing spinor on the auxiliary nine-manifold $Y:=X\times S^1$, where $S^1$ is a circle of constant radius, implying the reduction of the structure group of $Y$ to $Spin(7)$. In general, however, there is no reduction of the structure group of $X$ itself. This situation can be described in the language of generalized $Spin(7)$ structures, defined in terms of certain spinors of $Spin(TY\oplus T^*Y)$. We express the condition for ${\cal N}=1$ supersymmetry in terms of differential equations for these spinors. In an equivalent formulation, working locally in the vicinity of any point in $X$ in terms of a `preferred' $Spin(7)$ structure, we show that the requirement of ${\cal N}=1$ supersymmetry amounts to solving for the intrinsic torsion and all irreducible flux components, except for the one lying in the $\bf{27}$ of $Spin(7)$, in terms of the warp factor and a one-form $L$ on $X$ (not necessarily nowhere-vanishing) constructed as a $\xi$ bilinear; in addition, $L$ is constrained to satisfy a pair of differential equations. The formalism based on the group $Spin(7)$ is the most suitable language in which to describe supersymmetric compactifications on eight-manifolds of $Spin(7)$ structure, and/or small-flux perturbations around supersymmetric compactifications on manifolds of $Spin(7)$ holonomy.Comment: 24 pages. V2: introduction slightly extended, typos corrected in the text, references added. V3: the role of Spin(7) clarified, erroneous statements thereof corrected. New material on generalized Spin(7) structures in nine dimensions. To appear in JHE

Flexible Bioelectronic Devices Based on Micropatterned Monolithic Carbon Fiber Mats

Polymer-derived carbon can serve as an electrode material in multimodal neural stimulation, recording, and neurotransmitter sensing platforms. The primary challenge in its applicability in implantable, flexible neural devices is its characteristic mechanical hardness that renders it difficult to fabricate the entire device using only carbon. A microfabrication technique is introduced for patterning flexible, cloth-like, polymer-derived carbon fiber (CF) mats embedded in polyimide (PI), via selective reactive ion etching. This scalable, monolithic manufacturing method eliminates any joints or metal interconnects and creates electrocorticography electrode arrays based on a single CF mat. The batch-fabricated CF/PI composite structures, with critical dimension of 12.5 µm, are tested for their mechanical, electrical, and electrochemical stability, as well as to chemicals that mimic acute postsurgery inflammatory reactions. Their recording performance is validated in rat models. Reported CF patterning process can benefit various carbon microdevices that are expected to feature flexibility, material stability, and biocompatibility

A sigma model field theoretic realization of Hitchin's generalized complex geometry

We present a sigma model field theoretic realization of Hitchin's generalized complex geometry, which recently has been shown to be relevant in compactifications of superstring theory with fluxes. Hitchin sigma model is closely related to the well known Poisson sigma model, of which it has the same field content. The construction shows a remarkable correspondence between the (twisted) integrability conditions of generalized almost complex structures and the restrictions on target space geometry implied by the Batalin--Vilkovisky classical master equation. Further, the (twisted) classical Batalin--Vilkovisky cohomology is related non trivially to a generalized Dolbeault cohomology.Comment: 28 pages, Plain TeX, no figures, requires AMS font files AMSSYM.DEF and amssym.tex. Typos in eq. 6.19 and some spelling correcte