Chern-Simons Supergravity
Abstract
Three of the four fundamental forces of nature (electromagnetic, weak and
strong interactions) are described by gauge theories, that is, theories
which are invariant under a group of transformations acting at a point. Such systems are
best described in the language of fiber bundles, where the
fundamental physical object, the gauge field, is a Lie algebra-valued connection one-form
(local section). These theories have a quantum
formulation which can be explicitly constructed thanks to the fact that quantum mechanics
do not spoil the gauge symmetry.
The gravitational force is the oldest known to mankind and the least understood. It has a
symmetry very similar to -but not equivalent- to that
of a gauge theory: general coordinate invariance. The fact that this symmetry cannot be
described in terms of a fiber bundles might lie at the
heart of the fruitless search for a quantum theory of gravity that occupied some of the
best theoreticians for most of the XX century.
Chern-Simons theories, on the other hand, are naturally formulated on a fiber bundle and
are suitable for describing gravity in any odd number of
dimensions (d = 2n -1) as well as their supersymmetric extensions. For d > 3, these
theories have a topological origin as the potential for the Chern
classes in 2n dimensions but, unlike the d = 3 case, they are not "topological"
in the sense that they do possess propagating degrees of
freedom.
Index
Lectures
1.
CHERN-SIMONS GRAVITY: FROM (2+1)-DIMENSIONS TO (2N+1)- DIMENSIONS.
2. HIGHER DIMENSIONAL GRAVITY, PROPAGATING TORSION AND ADS GAUGE
INVARIANCE.
