Schild Action and Space-Time Uncertainty Principle in String Theory

TL;DR

This paper demonstrates the equivalence of Schild and Polyakov string quantizations and explores a novel interpretation of string theory as a quantized space-time framework with a minimum quantum of area, using matrix models.

Contribution

It establishes the equivalence of Schild and Polyakov quantizations and proposes a new interpretation of superstring theory as a quantized space-time with a minimal area quantum.

Findings

Schild action quantization is equivalent to Polyakov in critical dimensions

Interprets superstring theory as a quantized space-time framework

Proposes a microcanonical matrix model approach

Abstract

We show that the path-integral quantization of relativistic strings with the Schild action is essentially equivalent to the usual Polyakov quantization at critical space-time dimensions. We then present an interpretation of the Schild action which points towards a derivation of superstring theory as a theory of quantized space-time where the squared string scale plays the role of the minimum quantum for space-time areas. A tentative approach towards such a goal is proposed, based on a microcanonical formulation of large N supersymmetric matrix model.