The equations of motion on the M5-brane (the 6d (2,0)-superconformal QFT in a suitable limit) admits a soliton/black brane solution which is a string charged under the self-dual B-field [Howe, Lambert & West 1997, §3].
Externally this is the boundary of the M2-brane ending on the M5-brane. As such this is “the string in M-theory” and as such also called the M-string.
The elliptic genus of the self-dual string at the boundary of the M2-brane on the M5-brane has been suggested to be directly analogous to the Todd genus of the boundary of the open superstring ending on D-branes and hence has been suggested to be the M5-brane charge in Sati 2010. Discussion of the computation of this elliptic genus includes Hohenegger & Iqbal 2013.
Table of branes appearing in supergravity/string theory (for classification see at brane scan).
partition functions in quantum field theory as indices/genera/orientations in generalized cohomology theory:
The equations of motion of the self-dual string as a solution of D=6 supergravity was maybe first seen in
The appearance of self-dual string in six dimensions with an ADE classification was first observed in
As a black brane (“soliton”) solution to the equations of motion on the M5-brane:
As a Green-Schwarz sigma-model the brane scan-cocycle for the superstring in 6d is given in
Leonardo Castellani, Riccardo D'Auria, Pietro Fré, (III.7.15) of Supergravity and Superstrings - A Geometric Perspective, World Scientific, 1991
As the brane intersection of M2-branes onto an M5-brane:
Further discussion:
John Schwarz, Self-Dual Superstring in Six Dimensions [arXiv:hep-th/9604171]
Vasilis Niarchos, Konstadinos Siampos, Entropy of the self-dual string soliton, J. High Energ. Phys. 2012 134 (2012). [arXiv:1206.2935, doi:10.1007/JHEP07(2012)134]
Hisham Sati, Geometric and topological structures related to M-branes, part I, Proc. Symp. Pure Math. 81 (2010) 181-236 [arXiv:1001.5020]
In view of M-strings and the M-string elliptic genus:
Last revised on June 12, 2024 at 13:35:03. See the history of this page for a list of all contributions to it.