Light-Cone Gauge Quantization of Bosonic String Theories with Dilatons
This thesis develops light-cone gauge techniques within the Polyakov picture of string theory. Standard light-cone gauge formulations within the Nambu-Goto string are inappropriate for most modern string applications. The reformulation within the Polyakov picture opens up many new applications, including c = 1 non-critical 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 time-dependent 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 ghost-free light-cone gauge for the second order action in the Polyakov picture. The action is taken to be a general two-dimensional 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 light-cone gauge to be fixed. Also, the theory must be Weyl invariant. The conditions for Weyl invariance are computed within the light-cone gauge, reproducing the usual beta functions. The calculation of the dilaton beta function and the critical dimension is somewhat novel in this ghost-free theory. Some exactly solvable light-cone theories are discussed. The fourth chapter studies the subtle light-cone quantization of c = 1 non-critical 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.
- Pub Date:
- January 1992
- Physics: Elementary Particles and High Energy