12,825 research outputs found
On F-Algebroids and Dubrovin's Duality
In this note we introduce the concept of F-algebroid, and give its elementary
properties and some examples. We provide a description of the almost duality
for Frobenius manifolds, introduced by Dubrovin, in terms of a composition of
two anchor maps of a unique cotangent F-algebroid.Comment: 13 pages; v2 has small changes, it has improved exposition. Revised
version to appear in: "Archivum Mathematicum
Fermions via spinor-valued one-forms
Spinor-valued one-forms (Rarita-Schwinger fields) are normally used in the
context of supergravity, where they describe spin 3/2 particles (gravitinos).
Indeed, when decomposed into irreducible representations of the Lorentz group
such a field contains both a spin 1/2 and a spin 3/2 component, and the
Rarita-Schwinger Lagrangian is designed to make only the spin 3/2 propagate. We
point out that the opposite construction is also possible, and give a
spinor-valued one-form field Lagrangian that describes a propagating spin 1/2
particle.Comment: 23 pages, no figure
2D sigma models and differential Poisson algebras
We construct a two-dimensional topological sigma model whose target space is
endowed with a Poisson algebra for differential forms. The model consists of an
equal number of bosonic and fermionic fields of worldsheet form degrees zero
and one. The action is built using exterior products and derivatives, without
any reference to any worldsheet metric, and is of the covariant Hamiltonian
form. The equations of motion define a universally Cartan integrable system. In
addition to gauge symmetries, the model has one rigid nilpotent supersymmetry
corresponding to the target space de Rham operator. The rigid and local
symmetries of the action, respectively, are equivalent to the Poisson bracket
being compatible with the de Rham operator and obeying graded Jacobi
identities. We propose that perturbative quantization of the model yields a
covariantized differential star product algebra of Kontsevich type. We comment
on the resemblance to the topological A model.Comment: 20 page
- …