On the Schild action for D=0 and D=1 strings

TL;DR

This paper investigates the integration measure in the Schild matrix model for D=0 and D=1 strings, establishing its consistency with random lattice string models and ensuring a proper measure choice.

Contribution

It demonstrates how to fix the integration measure in the Schild matrix model by comparing it with random lattice string models for D=0 and D=1.

Findings

The measure can be fixed by comparison with D=0 models.

The fixed measure is consistent with D=1 case.

Provides a consistent framework for Schild matrix models.

Abstract

It is shown that the integration measure over the matrix $Y$ in the matrix representation of the Schild action can be fixed by comparing the Schild matrix model with the random lattice string model for D=0. It is further checked that the given measure is consistent with the case D=1 as well.