Reduction of open membrane moduli

TL;DR

This paper investigates how the open membrane metric reduces to open string parameters on D4-branes, revealing that only electric reductions yield the standard open string metric and coupling, while more general reductions describe bound states involving D2-branes.

Contribution

It introduces a general reduction framework for the open membrane metric, showing how different reduction choices lead to various open string and D-brane configurations, including bound states.

Findings

Electric reduction yields standard open string metric and coupling.

General reduction produces a rank 4 Born-Infeld tensor for bound states.

Open membrane noncommutativity reduces to open string noncommutativity under specific conditions.

Abstract

We perform a general reduction of the open membrane metric in a worldvolume direction of the M5-brane. Using reduction rules analogous to the bulk, we show that the open membrane metric leads to the standard open string metric and open string coupling constant on the D4-brane only for an ``electric'' reduction in which case the open membrane metric has no off-diagonal components and the Born-Infeld curvature tensor is a matrix of rank 2. Instead, if we perform a general reduction, with nonzero off-diagonal components of the open membrane metric, we obtain a rank 4 Born-Infeld tensor corresponding to a bound state of an open string with an open D2--brane. Next, we identify and reduce a 3-form open membrane ``noncommutativity'' tensor on the M5-brane. This open membrane parameter only reduces to the open string noncommutativity tensor on the D4-brane provided we constrain ourselves to an ``electric'' or a ``magnetic'' reduction.