Matrix Theory from Schild Action

TL;DR

This paper develops an alternative matrix theory formulation for membranes and p-branes starting from the Schild action, extending the BFSS matrix model to M-theory and providing a new perspective on membrane dynamics.

Contribution

It introduces a novel matrix model derived from the Schild action for p-branes, extending the type IIB matrix model to M-theory context.

Findings

Constructed Schild action for p-branes equivalent to Nambu-Goto action.

Derived a new matrix model related to M-theory's BFSS model.

Extended matrix model formulations from type IIB to M-theory.

Abstract

Starting from the Schild action for membrane, we present an alternative formulation of Matrix Theory. First of all, we construct the Schild action for general bosonic p-brane which is classically equivalent to the Nambu-Goto action for p-brane. Next, based on the constraint obtained from the variational equation for the auxiliary field in the case of $p = 2$ (membrane), we construct a new matrix model which is closely related to the matrix model of M-theory as developed by Banks, Fischler, Shenker and Susskind (BFSS). Our present formulation is a natural extension of the construction of type IIB matrix model by Yoneya to the case of M-theory.