Wrapped membranes, matrix string theory and an infinite dimensional Lie algebra

TL;DR

This paper explores the algebraic structure of matrix regularization for wrapped membranes in light-cone gauge, leading to a matrix string theory with specific boundary conditions, and embeds multi-wrapped membranes within this framework.

Contribution

It provides a concrete algebraic representation for wrapped membranes and constructs a corresponding matrix string theory without relying on prior duality arguments.

Findings

Derived a concrete algebraic representation for wrapped membranes.

Constructed a matrix string theory with boundary conditions for wrapped membranes.

Embedded multi-wrapped membrane configurations into matrix string theory.

Abstract

We examine the algebraic structure of the matrix regularization for the wrapped membrane on $R^{10}\times S^1$ in the light-cone gauge. We give a concrete representation for the algebra and obtain the matrix string theory having the boundary conditions for the matrix variables corresponding to the wrapped membrane, which is referred to neither Seiberg and Sen's arguments nor string dualities. We also embed the configuration of the multi-wrapped membrane in matrix string theory.