K. W. Xu

LIOUVILLE AND TODA SOLITONS IN M-THEORY

We study the general form of the equations for isotropic single-scalar, multi-scalar and dyonic p-branes in superstring theory and M-theory, and show that they can be cast into the form of Liouville, Toda (or Toda-like) equations. The general solutions describe non-extremal isotropic p-branes, reducing to the previously-known extremal solutions in limiting cases. In the non-extremal case, the dilatonic scalar fields are finite at the outer event horizon.

The complete cohomology of the string

We present a simple procedure for constructing the complete cohomology of the BRST operator of the two-scalar and multi-scalar strings. The method consists of obtaining two level-15 physical operators in the two-scalar string that are invertible, and that can normal order with all other physical operators. They can be used to map all physical operators into non-trivial physical operators whose momenta lie in a fundamental unit cell. By carrying out an exhaustive analysis of physical operators in this cell, the entire cohomology problem is solved.

The complete spectrum of the WN string

Abstract We obtain the complete physical spectrum of the WN string, for arbitrary N. The WN constraints freeze N−2 coordinates, while the remaining coordinates appear in the currents only via their energy-momentum tensor. The spectrum is then effectively described by a set of ordinary Virasoro-like string theories, but with a non-critical value for the central charge and a discrete set of non-standard values for the spin-2 intercepts. In particular, the physical spectrum of the WN string includes the usual massless states of the Virasoro string. By looking at the norms of low-lying states, we find strong indications that all the WN strings are unitary.

QUANTIZING HIGHER-SPIN STRING THEORIES

In this paper, we examine the conditions under which a higher-spin string theory can be quantized. The quantizability is crucially dependent on the way in which the matter currents are realized at the classical level. In particular, we construct classical realizations for the W2,s algebra, which is generated by a primary spin-s current in addition to the energy-momentum tensor, and discuss the quantization for s≤8. From these examples we see that quantum BRST operators can exist even when there is no quantum generalization of the classical W2,s algebra. Moreover, we find that there can be several inequivalent ways of quantizing a given classical theory, leading to different BRST operators with inequivalent cohomologies. We discuss their relation to certain minimal models. We also consider the hierarchical embeddings of string theories proposed recently by Berkovits and Vafa, and show how the already known W strings provide examples of this phenomenon. Attempts to find higher-spin fermionic generalizations lead us to examine whether classical BRST operators for (n odd) algebras can exist. We find that even though such fermionic algebras close up to null fields, one cannot build nilpotent BRST operators, at least of the standard form.

SL (∞,R) symmetry of quantum W∞ gravity

Abstract We examine the quantum theories of W ∞ gravity and W 1+∞ gravity, and show that they respectively exhibit SL (∞, R ) and GL (∞, R ) Kac-Moody symmetries. These symmetries generalise the SL (2, R ) Kac-Moody symmetry of light-cone two-dimensional quantum gravity, found by Polyakov.Two-dimensional gravity in the light-cone gauge was shown by Polyakov to exhibit an underlying

Embedding of the bosonic string into the W3 string

SL(2,R)

Canonical BRST quantisation of worldsheet gravities

Kac-Moody symmetry, which may be used to express the energy-momentum tensor for the metric component

Anomaly freedom and realisations for super-W3 strings

h_{++}

BRST operators for higher-spin algebras

in terms of the

Higher spin realizations of the bosonic string

SL(2,R)