Supersymmetric Quantum Mechanics for String-Bits

Abstract

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 $d=4$.

17 pages, Latex

References in corpus (6)

• Supersymmetry and Quantum Mechanics
• Reformulating String Theory with the $1/N$ Expansion
• String Bit Models for Superstring
• Calculating the Rest Tension for a Polymer of String Bits
• Super-Galilei Invariant Field Theories in 2+1 Dimensions
• Universality and Clustering in 1+1 Dimensional Superstring-Bit Models

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• Bit Strings from N=4 Gauge Theory
• PP-wave String Interactions from String Bit Model
• Light-Cone String Field Theory in a Plane Wave Background
• Stable String Bit Models
• Fermion Doubling and Berenstein--Maldacena--Nastase Correspondence
• The Nambu-Goto and Polyakov Strings via the Relativistic Particles