Symmetry Principles for String Theory

TL;DR

This paper explores the symmetry principles underlying string theory, focusing on gauge symmetries from automorphisms of conformal field theory algebras, revealing an infinite-dimensional supersymmetry algebra that unifies various symmetries.

Contribution

It introduces a framework connecting broken and unbroken symmetries in string theory through automorphisms, and identifies a weighted tensor algebra as a key subalgebra of the full symmetry.

Findings

Identification of an infinite-dimensional supersymmetry algebra including space-time diffeomorphisms

Unification of broken and unbroken symmetries within a common framework

Recognition of a weighted tensor algebra as a significant subalgebra

Abstract

The gauge symmetries that underlie string theory arise from inner automorphisms of the algebra of observables of the associated conformal field theory. In this way it is possible to study broken and unbroken symmetries on the same footing, and exhibit an infinite-dimensional supersymmetry algebra that includes space-time diffeomorphisms and an infinite number of spontaneously broken level-mixing symmetries. We review progress in this area, culminating in the identification of a weighted tensor algebra as a subalgebra of the full symmetry. We also briefly describe outstanding problems. Talk presented at the Gursey memorial conference, Istanbul, Turkey, June, 1994.