Fields and Symmetries of 2D Strings

Lectures presented at the Spring School, Trieste, Italy 1993.

At the present time, string theory (and its generalizations) remain relatively abstruse subjects to the particle phenomenologist and experimentalist. Yet, striking developments of the last two years offer hope that a fundamental non-perturbative formulation of this theory will be found, and that this formulation will permit us to make contact with supersymmetric standard-model physics. This article is based on a talk which attempted to convey the essence of these recent devel...

A review on topological strings and the geometry of the space of two dimensional theories. (Lectures given by C. Gomez at the Enrico Fermi Summer School, Varenna, July 1994)

We present a brief overview of 2-dim. string theory and its connection to the theory of non-relativistic fermions in one dimension. We emphasize (i) the role of $W_\infty$ algebra and (ii) the modelling of some aspects of 2-dim. black hole physics using the phase space representation of the fermi fluid.

We derive the $\sigma$-model tachyon $\beta$-function equation of 2-dimensional string theory, in the background of flat space and linear dilaton, working entirely within the $c=1$ matrix model. The tachyon $\beta$-function equation is satisfied by a \underbar{nonlocal} and \underbar{nonlinear} combination of the (massless) scalar field of the matrix model. We discuss the possibility of describing the `discrete states' as well as other possible gravitational and higher tensor...

As of today there exist consistent, gauge-invariant string field theories describing all string theories: bosonic open and closed strings, open superstrings, heterotic strings and type II strings. The construction of these theories require algebraic ingredients, such as $A_\infty$ and $L_\infty$ homotopy algebras, geometric ingredients, relevant to the building of moduli spaces of Riemann surfaces and the distribution of picture changing operators, and field-theoretic ingredi...

I review some of the recent progress in two-dimensional string theory, which is formulated as a sum over surfaces embedded in one dimension.

This is mainly a brief review of some key achievements in a `hot'' area of theoretical and mathematical physics. The principal aim is to outline the basic structures underlying {\em integrable} quantum field theory models with {\em infinite-dimensional} symmetry groups which display a radically new type of {\em quantum group} symmetries. Certain particular aspects are elaborated upon with some detail: integrable systems of Kadomtsev-Petviashvili type and their reductions appe...

The strong coupling physics of two dimensional gravity at $C=7$, $13$, $19$ is summarized. It is based on a new set of local fields which do not preserve chirality. Thus this quantum number becomes ``deconfined'' in the strongly coupled regime. This new set leads to a novel definition of the area elements, and hence to a modified expression for the string suceptibility, which the real part of the KPZ formula. It allows to define topological (strongly coupled ) Liouville strin...

We review some of the recent developments in the construction of $W$-string theories. These are generalisations of ordinary strings in which the two-dimensional ``worldsheet'' theory, instead of being a gauging of the Virasoro algebra, is a gauging of a higher-spin extension of the Virasoro algebra---a $W$ algebra. Despite the complexity of the (non-linear) $W$ algebras, it turns out that the spectrum can be computed completely and explicitly for more or less any $W$ string. ...