A Look at the Discretized Superstring Using Random Matrices

TL;DR

This paper investigates the discretized superstring using random matrix techniques, addressing the c=1 barrier and showing how fermionic embedding can stabilize the world sheet, potentially enabling a consistent higher-dimensional string theory.

Contribution

It introduces a novel approach combining random matrix methods with discretized superstring models to overcome the c=1 barrier and stabilize the world sheet.

Findings

Fermionic embedding can prevent world sheet degeneration.

Random matrix techniques provide insights into string stability.

Potential for a well-defined continuum string theory in higher dimensions.

Abstract

Beginning with a review of the arguments leading to the so-called c=1 barrier in the continuum formulation of noncritical string theory, the pathology is then exhibited in a discretized version of the theory, formulated through dynamical triangulation of two dimensional random surfaces. The effect of embedding the string in a superspace with fermionic coordinates is next studied in some detail. Using techniques borrowed from the theory of random matrices, indirect arguments are presented to establish that such an embedding may stabilize the two dimensional world sheet against degeneration into a branched polymer-like structure, thereby leading to a well-defined continuum string theory in a spacetime of dimension larger than 2.