Deformation independent open brane metrics and generalized theta parameters

TL;DR

This paper generalizes properties of open string metrics to open membranes and Dp-branes, deriving deformation-independent metrics and generalized theta parameters, with implications for background field dependence and lower-dimensional reductions.

Contribution

It introduces deformation-independent open brane metrics and generalized theta parameters, extending known string theory concepts to membranes and D-branes with new functional forms.

Findings

Derived explicit deformation-independent open membrane metrics.

Obtained generalized theta parameters as antisymmetric tensors.

Connected open membrane data to open string and D2-brane data via dimensional reduction.

Abstract

We investigate the consequences of generalizing certain well established properties of the open string metric to the conjectured open membrane and open Dp-brane metrics. By imposing deformation independence on these metrics their functional dependence on the background fields can be determined including the notorious conformal factor. In analogy with the non-commutativity parameter $\Theta^{\mu\nu}$ in the string case, we also obtain `generalized' theta parameters which are rank q+1 antisymmetric tensors (polyvectors) for open Dq-branes and rank 3 for the open membrane case. The expressions we obtain for the open membrane quantities are expected to be valid for general background field configurations, while the open D-brane quantities are only valid for one parameter deformations. By reducing the open membrane data to five dimensions, we show that they, modulo a subtlety with implications for the relation between OM-theory and NCYM, correctly generate the open string and open D2-data.