Stringy Instantons

A canonical Lorentz invariant field theory extension of collective field theory of d=1 matrix models is presented. We show that the low density, discrete, sector of collective field theory includes single eigenvalue Euclidean instantons which tunnel between different vacua of the extended theory. These "stringy" instantons induce non-perturbative effective operators of strength $e^{-{1/g}}$. The relationship of the world sheet description of string theory and Liouville theory to the effective space-time theory is explained.Comment: 12 pages, One figure not included, available as eps file on reques

S matrix of collective field theory

By applying the Lehmann-Symanzik-Zimmermann (LSZ) reduction formalism, we study the S matrix of collective field theory in which fermi energy is larger than the height of potential. We consider the spatially symmetric and antisymmetric boundary conditions. The difference is that S matrices are proportional to momenta of external particles in antisymmetric boundary condition, while they are proportional to energies in symmetric boundary condition. To the order of $g_{st}^2$, we find simple formulas for the S matrix of general potential. As an application, we calculate the S matrix of a case which has been conjectured to describe a "naked singularity".Comment: 19 page, LaTe

Matrix Theories from Reduced SU(N) Yang-Mills with Adjoint Fermions

We consider a dimensional reduction of 3+1 dimensional SU(N) Yang-Mills theory coupled to adjoint fermions to obtain a class of 1+1 dimensional matrix field theories. We derive the quantized light-cone Hamiltonian in the light-cone gauge A_- = 0 and large-N limit, and then solve for the masses, wavefunctions and structure functions of the color singlet ``meson-like'' and ``baryon-like'' boundstates. Among the states we study are many massless string-like states that can be solved for exactly.Comment: 13 pages, Revtex, one PS figur

Two-Dimensional String Theory, Topological Field Theories and the Deformed Matrix Model

In this paper the $c=1$ string theory is studied from the point of view of topological field theories. Calculations are done for arbitrary genus. A change in the prescription is proposed, which reproduces the results of the $1/x^2$ deformed matrix model. It is proposed that the deformed matrix model is related to a D-series Landau-Ginzburg superpotential.Comment: 20 pages, Latex CERN-TH.7155. Minor typos correcte

"Non-renormalization" without supersymmetry

The g_{YM} perturbed, non supersymmetric extension of the dual single matrix description of 1/2 BPS states, within the Hilbert space reduction to the oscillator subsector associated with chiral primaries is considered. This matrix model is described in terms of a single hermitean matrix. It is found that, apart from a trivial shift in the energy, the large N background, spectrum and interaction of invariant states are independent of g_{YM}. This property applies to more general D terms.Comment: latex, 14 pages; references added and correcte

Quantum and Classical Aspects of Deformed c=1c=1 Strings.

The quantum and classical aspects of a deformed $c=1$ matrix model proposed by Jevicki and Yoneya are studied. String equations are formulated in the framework of Toda lattice hierarchy. The Whittaker functions now play the role of generalized Airy functions in $c<1$ strings. This matrix model has two distinct parameters. Identification of the string coupling constant is thereby not unique, and leads to several different perturbative interpretations of this model as a string theory. Two such possible interpretations are examined. In both cases, the classical limit of the string equations, which turns out to give a formal solution of Polchinski's scattering equations, shows that the classical scattering amplitudes of massless tachyons are insensitive to deformations of the parameters in the matrix model.Comment: 52 pages, Latex