Fields and Symmetries of 2D Strings

The Ward identities of the $W_{\infty}$ symmetry in 2D string theory in the tachyon background are studied in the continuum approach. Comparing the solutions with the matrix model results, it is verified that 2D string amplitudes are different from the matrix model amplitudes only by the external leg factors even in higher genus. This talk is based on the recent work [1] and also [2] for the $c_M <1$ model. (Talk given at the workshop on ``Frontiers in Quantum Field Theory'',...

The field content of the two dimensional string theory consists of the dynamical tachyon field and some nonpropagating fields which consist in the topological sector of this theory. We propose in this paper to study this topological sector as a spacetime gauge theory with a simple centrally extended $w_\infty$ algebra. This $w_\infty$ algebra appears in both the world sheet BRST analysis and the matrix model approach. Since the two dimensional centrally extended Poincar\'e al...

(This talk was presented at the Third International Wigner Symposium on Group Theory, Oxford, September, 1993.) Matrix models provides us with the most powerful framework in which to analyze D=2 string theory, yet some of its miraculous features, such as discrete states and $w(\infty)$, remain rather obscure, because the string degrees of freedom have been removed. Liouville theory, on the other hand, has all its string degrees of freedom intact, yet is notoriously difficult ...

String theory in two-dimensional spacetime illuminates two main threads of recent development in string theory: (1) Open/closed string duality, and (2) Tachyon condensation. In two dimensions, many aspects of these phenomena can be explored in a setting where exact calculations can be performed. These lectures review the basic aspects of this system.

In this review article, we review the recent developments in constructing string field theories that have been proposed, all of which correctly reproduce the correlation functions of two-dimensional string theory. These include: (a) free fermion field theory (b) collective string field theory (c) temporal gauge string field theory (d) non-polynomial string field theory. We analyze discrete states, the $w(\infty)$ symmetry, and correlation functions in terms of these different...

This thesis is a study of two dimensional noncritical string theory. The main tool which is used, is the matrix model. Introductions to both the Liouville model and its matrix model formulation are included. In particular the special states are discussed. Some calculations of partition functions on genus one using field theory techniques are given. Nonperturbative issues and string theory at finite radius are discussed. Zero momentum correlation functions are calculated using...

We review some of the recent progress in the continuum formulation of two-dimensional string theory, i.e. two-dimensional quantum gravity coupled to $c=1$ matter. Special attention is devoted to the discrete states and to the $w_\infty$ algebra they generate. To demonstrate the power of the infinite symmetry, we use the $w_\infty$ Ward identities to derive recursion relations among certain classes of correlation functions, which allow to calculate them exactly. (Lectures deli...

I study the Ward identities of the $w_\infty$ symmetry of the two-dimensional string theory. It is found that, not just an isolated vertex operator, but also a number of vertex operators colliding at a point can produce local charge non-conservation. The structure of all such contact terms is determined. As an application, I calculate all the non-vanishing bulk tachyon amplitudes directly through the Ward identities for a Virasoro subalgebra of the $w_\infty$.

The Ward identities of the $W_{\infty}$ symmetry in two dimensional string theory in the tachyon background are studied in the continuum approach. We consider amplitudes different from 2D string ones by the external leg factor and derive the recursion relations among them. The recursion relations have non-linear terms which give relations among the amplitudes defined on different genus. The solutions agree with the matrix model results even in higher genus. We also discuss di...

We review some recent developments in the theory of $W_\infty$. We comment on its relevance to lower-dimensional string theory.