776 research outputs found
The Picard group of the moduli stack of stable hyperelliptic curves
We compute the Picard group of the moduli stack of stable hyperelliptic
curves of any genus, exhibiting explicit and geometrically meaningful
generators and relations.Comment: 6 pages, LaTeX; corrected minor errors, added reference
Corrections to the Abelian Born-Infeld Action Arising from Noncommutative Geometry
In a recent paper Seiberg and Witten have argued that the full action
describing the dynamics of coincident branes in the weak coupling regime is
invariant under a specific field redefinition, which replaces the group of
ordinary gauge transformations with the one of noncommutative gauge theory.
This paper represents a first step towards the classification of invariant
actions, in the simpler setting of the abelian single brane theory. In
particular we consider a simplified model, in which the group of noncommutative
gauge transformations is replaced with the group of symplectic diffeomorphisms
of the brane world volume. We carefully define what we mean, in this context,
by invariant actions, and rederive the known invariance of the Born-Infeld
volume form. With the aid of a simple algebraic tool, which is a generalization
of the Poisson bracket on the brane world volume, we are then able to describe
invariant actions with an arbitrary number of derivatives.Comment: 16 page
Some Computations with Seiberg-Witten Invariant Actions
We show, with a 2-dimensional example, that the low energy effective action
which describes the physics of a single D-brane is compatible with T-duality
whenever the corresponding U(N) non-abelian action is form-invariant under the
non-commutative Seiberg-Witten transformations.Comment: Contributions to the conference BRANE NEW WORLD and Noncommutative
Geometry, Torino, (Italy) Oct., 200
Matrix Representations of Holomorphic Curves on
We construct a matrix representation of compact membranes analytically
embedded in complex tori. Brane configurations give rise, via Bergman
quantization, to U(N) gauge fields on the dual torus, with
almost-anti-self-dual field strength. The corresponding U(N) principal bundles
are shown to be non-trivial, with vanishing instanton number and first Chern
class corresponding to the homology class of the membrane embedded in the
original torus. In the course of the investigation, we show that the proposed
quantization scheme naturally provides an associative star-product over the
space of functions on the surface, for which we give an explicit and
coordinate-invariant expression. This product can, in turn, be used the
quantize, in the sense of deformation quantization, any symplectic manifold of
dimension two.Comment: 29 page
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