Covariant Quantization of Heterotic Strings in Supersymmetric Chiral Boson Formulation

This dissertation presents the covariant supersymmetric chiral boson formulation of the heterotic strings. The main feature of this formulation is the covariant quantization of the so-called "leftons" and "rightons"--the (1,0) supersymmetric generalizations of the usual world-sheet chiral bosons, that constitute basic building blocks of general heterotic -type string models. Although the (Neveu-Schwarz-Ramond or Green-Schwarz) heterotic strings provide the most realistic string models, their covariant quantization, with the widely-used Siegel formalism, has never been rigorously carried out. Whether the Siegel formalism would lead to a consistent covariant quantization of heterotic strings has been extensively investigated. It is clarified in this dissertation that the covariant Siegel formalism is in fact pathological upon quantization. As a test, a general classical covariant (NSR) heterotic string action that has the Siegel symmetry is constructed in arbitrary curved space-time coupled to (1,0) world-sheet super-gravity. In the light-cone gauge quantization, the desired critical dimensions are derived for such an action with leftons and rightons compactified on group manifolds G_{L} times G_{R}. However, the covariant quantization of this action (with usual gauge-fixing procedure) does not agree with the physical results in the light-cone gauge quantization; in particular, some critical dimensions allowed in the light-cone gauge approach do not lead to the cancellation of both the Siegel and (super)conformal anomalies, required in the covariant approach. This dissertation establishes for the first time in the literature a new formalism for the covariant quantization of heterotic strings, which leads to the solution of the issue. A key step to this end is the covariant quantization of chiral bosons. Following the success of it, the desired consistent covariant path integral quantization of supersymmetric chiral bosons, and thus the general (NSR) heterotic-type strings with leftons and rightons compactified on torus otimes_{d_ L}S^1 timesotimes_{d_ R}S ^1 are carried out. In this new formalism, an infinite set of auxiliary (1,0) scalar superfields is introduced to convert the second-class chiral constraint into first-class ones. It turns out that the covariant gauge-fixed action has an extended BRST symmetry described by the graded algebra GL(1|1). A regularization respecting this symmetry is proposed to deal with the contributions of the infinite towers of auxiliary fields and associated ghosts and is verified to lead to the expected partition function. It is shown, in particular, that the (super)conformal anomalies from all unphysical degrees of freedom are cancelled, even in noncritical dimensions. The treatment is also free of a Siegel-type gauge anomaly, because of the use of linear chiral constraints.