Perturbation Theory in Two Dimensional Open String Field Theory

In this paper we develop the covariant string field theory approach to open 2d strings. Upon constructing the vertices, we apply the formalism to calculate the lowest order contributions to the 4- and 5- point tachyon--tachyon tree amplitudes. Our results are shown to match the `bulk' amplitude calculations of Bershadsky and Kutasov. In the present approach the pole structure of the amplitudes becomes manifest and their origin as coming from the higher string modes transparent.Comment: 26 page

Exact Solution of the One-Dimensional Non-Abelian Coulomb Gas at Large N

The problem of computing the thermodynamic properties of a one-dimensional gas of particles which transform in the adjoint representation of the gauge group and interact through non-Abelian electric fields is formulated and solved in the large $N$ limit. The explicit solution exhibits a first order confinement-deconfinement phase transition with computable properties and describes two dimensional adjoint QCD in the limit where matter field masses are large.Comment: 8 pages, late

Classical Solutions in Two-Dimensional String Theory and Gravitational Collapse

A general solution to the $D=2$ 1-loop beta functions equations including tachyonic back reaction on the metric is presented. Dynamical black hole (classical) solutions representing gravitational collapse of tachyons are constructed. A discussion on the correspondence with the matrix-model approach is given.Comment: 7 pages, UTTG-31-9

Systematic 1/N1/N corrections for bosonic and fermionic vector models without auxiliary fields

In this paper, colorless bilocal fields are employed to study the large $N$ limit of both fermionic and bosonic vector models. The Jacobian associated with the change of variables from the original fields to the bilocals is computed exactly, thereby providing an exact effective action. This effective action is shown to reproduce the familiar perturbative expansion for the two and four point functions. In particular, in the case of fermionic vector models, the effective action correctly accounts for the Fermi statistics. The theory is also studied non-perturbatively. The stationary points of the effective action are shown to provide the usual large $N$ gap equations. The homogeneous equation associated with the quadratic (in the bilocals) action is simply the two particle Bethe Salpeter equation. Finally, the leading correction in $1\over N$ is shown to be in agreement with the exact $S$ matrix of the model.Comment: 24 pages, uses REVTEX macros. Replaced with final version to appear in Phys. Rev.

Algebraic Structures and Eigenstates for Integrable Collective Field Theories

Conditions for the construction of polynomial eigen--operators for the Hamiltonian of collective string field theories are explored. Such eigen--operators arise for only one monomial potential $v(x) = \mu x^2$ in the collective field theory. They form a $w_{\infty}$--algebra isomorphic to the algebra of vertex operators in 2d gravity. Polynomial potentials of orders only strictly larger or smaller than 2 have no non--zero--energy polynomial eigen--operators. This analysis leads us to consider a particular potential $v(x)= \mu x^2 + g/x^2$. A Lie algebra of polynomial eigen--operators is then constructed for this potential. It is a symmetric 2--index Lie algebra, also represented as a sub--algebra of $U (s\ell (2)).$Comment: 27 page

On the spectrum of QCD(1+1) with large numbers of flavours N_F and colours N_C near N_F/N_C = 0

QCD(1+1) in the limit of a large number of flavours N_F and a large number of colours N_C is examined in the small N_F/N_C regime. Using perturbation theory in N_F/N_C, stringent results for the leading behaviour of the spectrum departing from N_F/N_C = 0 are obtained. These results provide benchmarks in the light of which previous truncated treatments of QCD(1+1) at large N_F and N_C are critically reconsidered.Comment: 6 revtex page

One-dimensional classical adjoint SU(2) Coulomb Gas

The equation of state of a one-dimensional classical nonrelativistic Coulomb gas of particles in the adjoint representation of SU(2) is given. The problem is solved both with and without sources in the fundamental representation at either end of the system. The gas exhibits confining properties at low densities and temperatures and deconfinement in the limit of high densities and temperatures. However, there is no phase transition to a regime where the string tension vanishes identically; true deconfinement only happens for infinite densities and temperatures. In the low density, low temperature limit, a new type of collective behavior is observed.Comment: 6 pages, 1 postscript figur

Numerical Simulations of N=(1,1) SYM{1+1} with Large Supersymmetry Breaking

We consider the $N=(1,1)$ SYM theory that is obtained by dimensionally reducing SYM theory in 2+1 dimensions to 1+1 dimensions and discuss soft supersymmetry breaking. We discuss the numerical simulation of this theory using SDLCQ when either the boson or the fermion has a large mass. We compare our result to the pure adjoint fermion theory and pure adjoint boson DLCQ calculations of Klebanov, Demeterfi, and Bhanot and of Kutasov. With a large boson mass we find that it is necessary to add additional operators to the theory to obtain sensible results. When a large fermion mass is added to the theory we find that it is not necessary to add operators to obtain a sensible theory. The theory of the adjoint boson is a theory that has stringy bound states similar to the full SYM theory. We also discuss another theory of adjoint bosons with a spectrum similar to that obtained by Klebanov, Demeterfi, and Bhanot.Comment: 12 pages, 4 figure

A Note on Background (In)dependence

In general quantum systems there are two kinds of spacetime modes, those that fluctuate and those that do not. Fluctuating modes have normalizable wavefunctions. In the context of 2D gravity and ``non-critical'' string theory these are called macroscopic states. The theory is independent of the initial Euclidean background values of these modes. Non-fluctuating modes have non-normalizable wavefunctions and correspond to microscopic states. The theory depends on the background value of these non-fluctuating modes, at least to all orders in perturbation theory. They are superselection parameters and should not be minimized over. Such superselection parameters are well known in field theory. Examples in string theory include the couplings $t_k$ (including the cosmological constant) in the matrix models and the mass of the two-dimensional Euclidean black hole. We use our analysis to argue for the finiteness of the string perturbation expansion around these backgrounds.Comment: 16 page

1+11+1-Dimensional Large NN QCD coupled to Adjoint Fermions

We consider 1+1-dimensional QCD coupled to Majorana fermions in the adjoint representation of the gauge group $SU(N)$. Pair creation of partons (fermion quanta) is not suppressed in the large-$N$ limit, where the glueball-like bound states become free. In this limit the spectrum is given by a linear \lc\ Schr\" odinger equation, which we study numerically using the discretized \lcq. We find a discrete spectrum of bound states, with the logarithm of the level density growing approximately linearly with the mass. The wave function of a typical excited state is a complicated mixture of components with different parton numbers. A few low-lying states, however, are surprisingly close to being eigenstates of the parton number, and their masses can be accurately calculated by truncated diagonalizations.Comment: 22 pages + 9 figures (available by request from [email protected]), uses phyzzx.tex + tables.tex PUPT-1413, IASSNS-HEP-93/4