Universality and Clustering in 1+1 Dimensional Superstring-Bit Models

We construct a 1+1 dimensional superstring-bit model for D=3 Type IIB superstring. This low dimension model escapes the problems encountered in higher dimension models: (1) It possesses full Galilean supersymmetry; (2) For noninteracting polymers of bits, the exactly soluble linear superpotential describing bit interactions is in a large universality class of superpotentials which includes ones bounded at spatial infinity; (3) The latter are used to construct a superstring-bit model with the clustering properties needed to define an $S$-matrix for closed polymers of superstring-bits.Comment: 11 pages, Latex documen

String Bit Models for Superstring

We extend the model of string as a polymer of string bits to the case of superstring. We mainly concentrate on type II-B superstring, with some discussion of the obstacles presented by not II-B superstring, together with possible strategies for surmounting them. As with previous work on bosonic string we work within the light-cone gauge. The bit model possesses a good deal less symmetry than the continuous string theory. For one thing, the bit model is formulated as a Galilei invariant theory in $(D-2)+1$ dimensional space-time. This means that Poincar\'e invariance is reduced to the Galilei subgroup in $D-2$ space dimensions. Naturally the supersymmetry present in the bit model is likewise dramatically reduced. Continuous string can arise in the bit models with the formation of infinitely long polymers of string bits. Under the right circumstances (at the critical dimension) these polymers can behave as string moving in $D$ dimensional space-time enjoying the full $N=2$ Poincar\'e supersymmetric dynamics of type II-B superstring.Comment: 43 pages, phyzzx require

Supersymmetric Quantum Mechanics for String-Bits

We develop possible versions of supersymmetric single particle quantum mechanics, with application to superstring-bit models in view. We focus principally on space dimensions $d=1,2,4,8$, the transverse dimensionalities of superstring in $3,4,6,10$ space-time dimensions. These are the cases for which ``classical'' superstring makes sense, and also the values of $d$ for which Hooke's force law is compatible with the simplest superparticle dynamics. The basic question we address is: When is it possible to replace such harmonic force laws with more general ones, including forces which vanish at large distances? This is an important question because forces between string-bits that do not fall off with distance will almost certainly destroy cluster decomposition. We show that the answer is affirmative for $d=1,2$, negative for $d=8$, and so far inconclusive for $d=4$.Comment: 17 pages, Late

Quantum Newtonian Dynamics on a Light Front

We recall the special features of quantum dynamics on a light-front (in an infinite momentum frame) in string and field theory. The reason this approach is more effective for string than for fields is stressed: the light-front dynamics for string is that of a true Newtonian many particle system, since a string bit has a fixed Newtonian mass. In contrast, each particle of a field theory has a variable Newtonian mass P^+, so the Newtonian analogy actually requires an infinite number of species of elementary Newtonian particles. This complication substantially weakens the value of the Newtonian analogy in applying light-front dynamics to nonperturbative problems. Motivated by the fact that conventional field theories can be obtained as infinite tension limits of string theories, we propose a way to recast field theory as a standard Newtonian system. We devise and analyze some simple quantum mechanical systems that display the essence of the proposal, and we discuss prospects for applying these ideas to large N_c QCD.Comment: 13 pages, 3 figures, LaTex, psfig, references added, APS copyrigh

Calculating the Rest Tension for a Polymer of String Bits

We explore the application of approximation schemes from many body physics, including the Hartree-Fock method and random phase approximation (RPA), to the problem of analyzing the low energy excitations of a polymer chain made up of bosonic string bits. We accordingly obtain an expression for the rest tension $T_0$ of the bosonic relativistic string in terms of the parameters characterizing the microscopic string bit dynamics. We first derive an exact connection between the string tension and a certain correlation function of the many-body string bit system. This connection is made for an arbitrary interaction potential between string bits and relies on an exact dipole sum rule. We then review an earlier calculation by Goldstone of the low energy excitations of a polymer chain using RPA. We assess the accuracy of the RPA by calculating the first order corrections. For this purpose we specialize to the unique scale invariant potential, namely an attractive delta function potential in two (transverse) dimensions. We find that the corrections are large, and discuss a method for summing the large terms. The corrections to this improved RPA are roughly 15\%.Comment: 44 pages, phyzzx, psfig required, Univ. of Florida preprint, UFIFT-HEP-94

Bag Model for a Link in a Closed Gluonic Chain

The large $N_c$ limit of Yang-Mills gauge theory is the dynamics of a closed gluonic chain, but this fact does not obviate the inherently strong coupling nature of the dynamical problem. However, we suggest that a single link in such a chain might be reasonably described in the quasi-perturbative language of gluons and their interactions. To implement this idea, we use the MIT bag to model the physics of a nearest neighbor bond.Comment: 10 pages, LaTe

More On The Connection Between Planar Field Theory And String Theory

We continue work on the connection between world sheet representation of the planar phi^3 theory and string formation. The present article, like the earlier work, is based on the existence of a solitonic solution on the world sheet, and on the zero mode fluctuations around this solution. The main advance made in this paper is the removal of the cutoff and the transition to the continuum limit on the world sheet. The result is an action for the modes whose energies remain finite in this limit (light modes). The expansion of this action about a dense background of graphs on the world sheet leads to the formation of a string.Comment: 27 pages, 3 figure

Field Theory On The World Sheet: Improvements And Generalizations

This article is the continuation of a project of investigating planar phi^3 model in various dimensions. The idea is to reformulate them on the world sheet, and then to apply the classical (meanfield) approximation, with two goals: To show that the ground state of the model is a solitonic configuration on the world sheet, and the quantum fluctuations around the soliton lead to the formation of a transverse string. After a review of some of the earlier work, we introduce and discuss several generalizations and new results. In 1+2 dimensions, a rigorous upper bound on the solitonic energy is established. A phi^4 interaction is added to stabilize the original phi^3 model. In 1+3 and 1+5 dimensions, an improved treatment of the ultraviolet divergences is given. And significantly, we show that our approximation scheme can be imbedded into a systematic strong coupling expansion. Finally, the spectrum of quantum fluctuations around the soliton confirms earlier results: In 1+2 and 1+3 dimensions, a transverse string is formed on the world sheet.Comment: 29 pages, 5 figures, several typos and eqs.(74) and (75) are corrected, a comment added to section

A Six Vertex Model on a Fishnet

The flow of U(1) charge through dense fishnet diagrams, in a non-hermitian matrix scalar field theory g_1Tr(\Sigma^\dagger\Sigma)^2 + 2g_1vTr\Sigma^{\dagger 2}\Sigma^2, is described by a 6-vertex model on a ``diamond'' lattice [1]. We give a direct calculation of the continuum properties of the 6-vertex model on this novel lattice, explicitly confirming the conclusions of [1], that, for 1/2 < v< \infty, they are identical to those of a world-sheet scalar field compactified on a circle S_1. The radius of the circle is related to the ratio v of quartic couplings by R^{-2} = 2T_0 arccos(1-1/2v^2). This direct computational approach may be of value in generalizing the conclusions to the non-Abelian O(n) case.Comment: latex, 14 pages, 3 figure

PP-wave String Interactions from String Bit Model

We construct the string states $|O_{p}^J>_J$, $|O_{q}^{J_1}>_{{J_1}{J_2}}$ and $|O_{0}^{J_{1}J_{2}}>_{{J_1}{J_2}}$ in the Hilbert space of the quantum mechanical orbifold model so as to calculate the three point functions and the matrix elements of the light-cone Hamiltonian from the interacting string bit model. With these string states we show that the three point functions and the matrix elements of the Hamiltonian derived from the interacting string bit model up to $g^{2}_2$ order precisely match with those computed from the perturbative SYM theory in BMN limit.Comment: 20 pages, no figure, LaTeX, some changes made and references adde