369 research outputs found
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
Cosmological string models from Milne spaces and SL(2,Z) orbifold
The -dimensional Milne Universe with extra free directions is used to
construct simple FRW cosmological string models in four dimensions, describing
expansion in the presence of matter with , . We then
consider the n=2 case and make SL(2,Z) orbifold identifications. The model is
surprisingly related to the null orbifold with an extra reflection generator.
The study of the string spectrum involves the theory of harmonic functions in
the fundamental domain of SL(2,Z). In particular, from this theory one can
deduce a bound for the energy gap and the fact that there are an infinite
number of excitations with a finite degeneracy. We discuss the structure of
wave functions and give examples of physical winding states becoming light near
the singularity.Comment: 14 pages, harvma
Open-String Actions and Noncommutativity Beyond the Large-B Limit
In the limit of large, constant B-field (the ``Seiberg-Witten limit''), the
derivative expansion for open-superstring effective actions is naturally
expressed in terms of the symmetric products *n. Here, we investigate
corrections around the large-B limit, for Chern-Simons couplings on the brane
and to quadratic order in gauge fields. We perform a boundary-state computation
in the commutative theory, and compare it with the corresponding computation on
the noncommutative side. These results are then used to examine the possible
role of Wilson lines beyond the Seiberg-Witten limit. To quadratic order in
fields, the entire tree-level amplitude is described by a metric-dependent
deformation of the *2 product, which can be interpreted in terms of a deformed
(non-associative) version of the Moyal * product.Comment: 30 pages, harvma
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