New Principles for String/Membrane Unification

TL;DR

This paper proposes a unifying framework based on self-dual geometries in 2+2 dimensions that connects various string theories and supermembrane models across different dimensions, offering new insights into their fundamental structure.

Contribution

It introduces a novel unifying approach using 2+2 dimensional self-dual geometries to connect diverse string and membrane theories in different dimensions.

Findings

Unified description of string theories in 1+1 and 2+1 dimensions

Connection between N=(2,1) heterotic string and supermembranes

Potential insights into fundamental degrees of freedom of string theories

Abstract

The target space theory of the N=(2,1) heterotic string may be interpreted as a theory of gravity coupled to matter in either $1+1$ or $2+1$ dimensions. Among the target space theories in $1+1$ dimensions are the bosonic, type II, and heterotic string world sheet field theories in a physical gauge. The $2+1$ dimensional version describes a consistent quantum theory of supermembranes in $10+1$ dimensions. The unifying framework for all of these vacua is a theory of $2+2$ dimensional self-dual geometries embedded in $10+2$ dimensions. There are also indications that the N=(2,1) string describes the strong coupling dynamics of compactifications of critical string theories to two dimensions, and may lead to insights about the fundamental degrees of freedom of the theory.