9 research outputs found
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
Symmetry, Gravity and Noncommutativity
We review some aspects of the implementation of spacetime symmetries in
noncommutative field theories, emphasizing their origin in string theory and
how they may be used to construct theories of gravitation. The geometry of
canonical noncommutative gauge transformations is analysed in detail and it is
shown how noncommutative Yang-Mills theory can be related to a gravity theory.
The construction of twisted spacetime symmetries and their role in constructing
a noncommutative extension of general relativity is described. We also analyse
certain generic features of noncommutative gauge theories on D-branes in curved
spaces, treating several explicit examples of superstring backgrounds.Comment: 52 pages; Invited review article to be published in Classical and
Quantum Gravity; v2: references adde
Formal Lagrangian Operad
Given a symplectic manifold M, we may define an operad structure on the the spaces Ok of
the Lagrangian submanifolds of Mk × M via symplectic reduction. If M is also a symplectic
groupoid, then its multiplication space is an associative product in this operad. Following this
idea, we provide a deformation theory for symplectic groupoids analog to the deformation theory
of algebras. It turns out that the semiclassical part of Kontsevich’s deformation of C∞d is a
deformation of the trivial symplectic groupoid structure of T∗d