Making Non-Associative Algebra Associative

TL;DR

This paper demonstrates that an associative algebra from earlier work can reproduce correlation functions in a nonassociative algebra context for D-branes, addressing gauge transformation issues in noncommutative spaces.

Contribution

It shows the equivalence of associative and nonassociative algebras in modeling D-brane correlation functions and proposes a generalized gauge transformation framework.

Findings

Associative algebra reproduces nonassociative correlation functions.

Functions on D-branes do not form a closed algebra.

Generalized gauge transformations involve global symmetries.

Abstract

Based on results about open string correlation functions, a nonassociative algebra was proposed in a recent paper for D-branes in a background with nonvanishing $H$. We show that our associative algebra obtained by quantizing the endpoints of an open string in an earlier work can also be used to reproduce the same correlation functions. The novelty of this algebra is that functions on the D-brane do not form a closed algebra. This poses a problem to define gauge transformations on such noncommutative spaces. We propose a resolution by generalizing the description of gauge transformations which naturally involves global symmetries. This can be understood in the context of matrix theory.