It is shown that the global charges of a gauge theory may yield a nontrivial central extension of the asymptotic symmetry algebra already at the classical level. This is done by studying three dimensional gravity with a negative cosmological constant. The asymptotic symmetry group in that case is eitherR×SO(2) or the pseudo-conformal group in two dimensions, depending on the boundary conditions adopted at spatial infinity. In the latter situation, a nontrivial central charge appears in the algebra of the canonical generators, which turns out to be just the Virasoro central charge.

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Central Charges in the Canonical Realization of Asymptotic Symmetries: An Example from Three-Dimensional Gravity

http://inspirehep.net/record/393570/files/arXiv:hep-th_9503124.pdf

String theory dynamics in various dimensions

Vacuum configurations for superstrings

A generalization of Einstein's gravitational theory is discussed in which the spin of matter as well as its mass plays a dynamical role. The spin of matter couples to a non-Riemannian structure in space-time, Cartan's torsion tensor. The theory which emerges from taking this coupling into account, the ${U}_{4}$ theory of gravitation, predicts, in addition to the usual infinite-range gravitational interaction medicated by the metric field, a new, very weak, spin contact interaction of gravitational origin. We summarize here all the available theoretical evidence that argues for admitting spin and torsion into a relativistic gravitational theory. Not least among this evidence is the demonstration that the ${U}_{4}$ theory arises as a local gauge theory for the Poincar\'e group in space-time. The deviations of the ${U}_{4}$ theory from standard general relativity are estimated, and the prospects for further theoretical development are assessed.

/pdf/general-relativity-with-spin-and-torsion-foundations-and-2tppss7mai.pdf

General Relativity with Spin and Torsion: Foundations and Prospects

This article reviews the generalization of field theory to space-time with noncommuting coordinates, starting with the basics and covering most of the active directions of research. Such theories are now known to emerge from limits of M theory and string theory and to describe quantum Hall states. In the last few years they have been studied intensively, and many qualitatively new phenomena have been discovered, on both the classical and the quantum level.

Joel Scherk

Papers

Supergravity in theory in 11 dimensions

How to get masses from extra dimensions

Supersymmetric Yang-Mills Theories

Supersymmetry, supergravity theories and the dual spinor model

Spontaneous breaking of supersymmetry through dimensional reduction