An M-theory solution generating technique and SL(2,R)

TL;DR

This paper extends solution generating techniques from string theory to M-theory, enabling direct deformation of M5-branes via three-form fields and revealing connections to SL(2,R) transformations, with implications for noncommutative geometry.

Contribution

It introduces a new M-theory solution generating method that generalizes existing techniques and relates M5-brane deformations to SL(2,R) transformations, also extending to NS5-branes in string theory.

Findings

Deformation of M5-branes corresponds to SL(2,R) transformations.

Open membrane metric remains deformation independent under certain conditions.

Derived covariant expression for open D2-brane coupling in OD2-theory.

Abstract

In this paper we generalize the O(p+1,p+1) solution generating technique (this is a method used to deform Dp-branes by turning on a NS-NS B-field) to M-theory, in order to be able to deform M5-brane supergravity solutions directly in eleven dimensions, by turning on a non zero three form A. We find that deforming the M5-brane, in some cases, corresponds to performing certain SL(2,R) transformations of the Kahler structure parameter for the three-torus, on which the M5-brane has been compactified. We show that this new M-theory solution generating technique can be reduced to the O(p+1,p+1) solution generating technique with p=4. Further, we find that it implies that the open membrane metric and generalized noncommutativity parameter are manifestly deformation independent for electric and light-like deformations. We also generalize the O(p+1,p+1) method to the type IIA/B NS5-brane in order to be able to deform NS5-branes with RR three and two forms, respectively. In the type IIA case we use the newly obtained solution generating technique and deformation independence to derive a covariant expression for an open D2-brane coupling, relevant for OD2-theory.