LightCone Gauge Quantization of Bosonic String Theories with Dilatons
Abstract
This thesis develops lightcone gauge techniques within the Polyakov picture of string theory. Standard lightcone gauge formulations within the NambuGoto string are inappropriate for most modern string applications. The reformulation within the Polyakov picture opens up many new applications, including c = 1 noncritical strings and sigma models with compactification propagation. The first chapter provides an introduction to the thesis. The second chapter discusses compactification propagation. A new class of timedependent background space configurations is shown to be exact classical string vacua. These vacua have variations in the geometry of the compactified internal space propagating through the uncompactified space at the speed of light. These stringy gravitational waves (of arbitrary amplitude) are accompanied by a specific dilaton wave. All the moduli in toroidal compactification can depend on time in this way consistently. The question of whether variations in the moduli of more complicated static vacua can propagate is also examined. Many of the spaces generated like this are explicit string vacua, without readjustment at higher orders in alpha^ '. The third chapter describes the formulation of the manifestly ghostfree lightcone gauge for the second order action in the Polyakov picture. The action is taken to be a general twodimensional sigma model, giving a bosonic string theory with spacetime metric, antisymmetric tensor, dilaton and tachyon fields. These fields are found to require a symmetry generated by a null, covariantly constant spacetime vector in order for the lightcone gauge to be fixed. Also, the theory must be Weyl invariant. The conditions for Weyl invariance are computed within the lightcone gauge, reproducing the usual beta functions. The calculation of the dilaton beta function and the critical dimension is somewhat novel in this ghostfree theory. Some exactly solvable lightcone theories are discussed. The fourth chapter studies the subtle lightcone quantization of c = 1 noncritical strings. The light cone gauge quantum mechanics is developed, resolving an unusual gauge singularity which would remove the special states from the physical Hilbert space. Some aspects of the interacting theory are also discussed. An appendix describes a new solution to field theory with quadratic Hamiltonians.
 Publication:

Ph.D. Thesis
 Pub Date:
 January 1992
 Bibcode:
 1992PhDT........96R
 Keywords:

 COMPACTIFICATION;
 Physics: Elementary Particles and High Energy