From noncommutative string/membrane to ordinary ones

TL;DR

This paper explores the theoretical equivalence between noncommutative and commutative models in string and membrane theories, analyzing the conditions and transformations that lead to commutative coordinates in various string theory setups.

Contribution

It provides a detailed analysis of how noncommutative string and membrane models can be transformed into equivalent commutative models through variable changes and constraint conversions.

Findings

Change of variables yields commuting coordinates in decoupling limit

Constraints can be converted to achieve commutativity without decoupling

Noncommutative M-5-brane models can be equivalent to commutative ones

Abstract

We discuss origin of equivalence between noncommutative and ordinary Yang-Mills from point of view of string theory. Working in BRST/Hamiltonian framework first we investigate string model in the decoupling limit and show that change of variables and applying the conversion of constraints of decoupled string theory gives commuting coordinates on the D-brane. Also, we discuss algebra of constraints in general case and show the ways of having commutative coordinates without going to decoupling limit. It could be argued that noncommutative string in B-field is equivalent to the commutative model. We investigate the case of the membrane ending on the M-5-brane in constant C-field and discuss noncommutative/commutative equivalence in this case.