5 research outputs found
A spinor approach to Walker geometry
A four-dimensional Walker geometry is a four-dimensional manifold M with a
neutral metric g and a parallel distribution of totally null two-planes. This
distribution has a natural characterization as a projective spinor field
subject to a certain constraint. Spinors therefore provide a natural tool for
studying Walker geometry, which we exploit to draw together several themes in
recent explicit studies of Walker geometry and in other work of Dunajski (2002)
and Plebanski (1975) in which Walker geometry is implicit. In addition to
studying local Walker geometry, we address a global question raised by the use
of spinors.Comment: 41 pages. Typos which persisted into published version corrected,
notably at (2.15
Noncommutative Electromagnetism As A Large N Gauge Theory
We map noncommutative (NC) U(1) gauge theory on R^d_C X R^{2n}_{NC} to U(N ->
\infty) Yang-Mills theory on R^d_C, where R^d_C is a d-dimensional commutative
spacetime while R^{2n}_{NC} is a 2n-dimensional NC space. The resulting U(N)
Yang-Mills theory on R^d_C is equivalent to that obtained by the dimensional
reduction of (d+2n)-dimensional U(N) Yang-Mills theory onto R^d_C. We show that
the gauge-Higgs system (A_\mu,\Phi^a) in the U(N -> \infty) Yang-Mills theory
on R^d_C leads to an emergent geometry in the (d+2n)-dimensional spacetime
whose metric was determined by Ward a long time ago. In particular, the
10-dimensional gravity for d=4 and n=3 corresponds to the emergent geometry
arising from the 4-dimensional N=4 vector multiplet in the AdS/CFT duality. We
further elucidate the emergent gravity by showing that the gauge-Higgs system
(A_\mu,\Phi^a) in half-BPS configurations describes self-dual Einstein gravity.Comment: 25 pages; More clarifications, to appear in Eur. Phys. J.
Born-Infeld Theory and Stringy Causality
Fluctuations around a non-trivial solution of Born-Infeld theory have a
limiting speed given not by the Einstein metric but the Boillat metric. The
Boillat metric is S-duality invariant and conformal to the open string metric.
It also governs the propagation of scalars and spinors in Born-Infeld theory.
We discuss the potential clash between causality determined by the closed
string and open string light cones and find that the latter never lie outside
the former. Both cones touch along the principal null directions of the
background Born-Infeld field. We consider black hole solutions in situations in
which the distinction between bulk and brane is not sharp such as space filling
branes and find that the location of the event horizon and the thermodynamic
properties do not depend on whether one uses the closed or open string metric.
Analogous statements hold in the more general context of non-linear
electrodynamics or effective quantum-corrected metrics. We show how Born-Infeld
action to second order might be obtained from higher-curvature gravity in
Kaluza-Klein theory. Finally we point out some intriguing analogies with
Einstein-Schr\"odinger theory.Comment: 31 pages, 4 figures, LaTex; Some comments and references adde