Homogeneous plane waves
Abstract
Motivated by the search for potentially exactly solvable timedependent string backgrounds, we determine all homogeneous plane wave (HPW) metrics in any dimension and find one family of HPWs with geodesically complete metrics and another with metrics containing null singularities. The former generalises both the CahenWallach (constant A_{ij}) metrics to timedependent HPWs, A_{ij}( x^{+}), and the OzsvathSchücking antiMach metric to arbitrary dimensions. The latter is a generalisation of the known homogeneous metrics with A_{ij}̃1/( x^{+}) ^{2} to a more complicated timedependence. We display these metrics in various coordinate systems, show how to embed them into string theory, and determine the isometry algebra of a general HPW and the associated conserved charges. We review the LewisRiesenfeld theory of invariants of timedependent harmonic oscillators and show how it can be deduced from the geometry of plane waves. We advocate the use of the invariant associated with the extra (timelike) isometry of HPWs for lightcone quantisation, and illustrate the procedure in some examples.
 Publication:

Nuclear Physics B
 Pub Date:
 March 2003
 DOI:
 10.1016/S05503213(03)000555
 arXiv:
 arXiv:hepth/0212135
 Bibcode:
 2003NuPhB.654..135B
 Keywords:

 High Energy Physics  Theory;
 General Relativity and Quantum Cosmology
 EPrint:
 48 pages, LaTeX2e, v2: additional references and cosmetic corrections