Fields and Symmetries of 2D Strings

This is an editorial summary of the contents of a Book comprising a set of Articles by acknowledged experts dealing with the impact of Field Theory on major areas of physics (from elementary particles through condensed matter to strings), arranged subjectwise under six broad heads. The Book which emphasizes the conceptual, logical and formal aspects of the state of the art in these respective fields, carries a Foreword by Freeman Dyson, and is to be published by the Indian Na...

We find the precise relationship between the loop gas method and the matrix quantum mechanics approach to two-dimensional string theory. The two systems are distinguished by different target spaces ($\Z$ and $\R$, respectively) as far as {\it observables} are concerned. We argue that target space loop correlators should coincide in the two models and demonstrate this for a number of examples. As a consequence some interesting generic observations about the structure of two-di...

An infinite number of distinct $d=1$ matrix models reproduce the perturbation theory of $d=2$ string theory. Due to constraints of causality, however, we argue that none of the existing constructions gives a consistent nonperturbative definition of the $d=2$ string.

In a recent paper, Balthazar, Rodriguez and Yin found some remarkable agreement between the results of c=1 matrix model and D-instanton corrections in two dimensional string theory. Their analysis left undetermined two constants in the string theory computation which had to be fixed by comparing the results with the matrix model results. One of these constants is affected by possible renormalization of the D-instanton action that needs to be computed separately. In this paper...

We derive a Kontsevich-type matrix model for the c=1 string directly from the W-infinity solution of the theory. The model that we obtain is different from previous proposals, which are proven to be incorrect. Our matrix model contains the Penner and Kontsevich cases, and we study its quantum effective action. The simplicity of our model leads to an encouraging interpretation in the context of background-independent noncritical string field theory.

String theory builds on the great legacy of Yukawa and Tomonaga: New degrees of freedom and control of the UV are two important themes. This talk will give an overview of some of the progress and some of the unsolved problems that characterize string theory today. It is divided into two parts: (1) Connecting String Theory to the Real World; (2) Gauge Theory/String Theory Duality. Two other major subjects, which I will omit, are Black Holes in String Theory and The Impact of S...

We discuss different formulations and approaches to string theory and $ 2d$ quantum gravity. The generic idea to get a unique description of {\it many} different string vacua altogether is demonstrated on the examples in $ 2d$ conformal, topological and matrix formulations. The last one naturally brings us to the appearance of classical integrable systems in string theory. Physical meaning of the appearing structures is discussed and some attempts to find directions of possib...

The string theory defined by gauging $\W_{\infty/2}$, the sub-algebra of $\W_{\infty}$ generated by the currents of even spin, is discussed. The critical value of the central charge is calculated using zeta-function techniques and shown to be $c=1$. A critical string theory is constructed by coupling a free boson to $\W_{\infty/2}$-gravity and the physical states are analysed.

On the basis of an area-preserving symmetry in the phase space of a one-dimensional matrix model - believed to describe two-dimensional string theory in a black-hole background which also allows for space-time foam - we give a geometric interpretation of the fact that two-dimensional stringy black holes are consistent with conventional quantum mechanics due to the infinite gauged `W-hair' property that characterises them.

Minor corrections made and several references changed.