Contents

# Contents

## Idea

The brane intersection of an M2-brane with an M5-brane (i.e. a self-dual string in the M5’s worldvolume D=6 N=(2,0) SCFT is called an M-string if the other end of the M2-brane intersects another, parallel, M5-brane.

graphics grabbed from HLV 14

In contrast, if the other end of the M2 intersects an MO9-plane, then the former intersection is an E-string.

## Properties

### M-string elliptic genus

See at M-string elliptic genus.

brane intersections/bound states/wrapped branes/polarized branes

S-duality$\,$bound states:

intersecting$\,$M-branes:

## References

### Elliptic genera as super $p$-brane partition functions

The interpretation of elliptic genera (especially the Witten genus) as the partition function of a 2d superconformal field theory (or Landau-Ginzburg model) – and especially of the heterotic string (“H-string”) or type II superstring worldsheet theory has precursors in

and then strictly originates with:

Review in:

#### Formulations

##### Via super vertex operator algebra

Formulation via super vertex operator algebras:

and for the topologically twisted 2d (2,0)-superconformal QFT (the heterotic string with enhanced supersymmetry) via sheaves of vertex operator algebras in

based on chiral differential operators:

##### Via Dirac-Ramond operators on free loop space

Tentative interpretation as indices of Dirac-Ramond operators as would-be Dirac operators on smooth loop space:

##### Via conformal nets

Tentative formulation via conformal nets:

#### Conjectural interpretation in tmf-cohomology

The resulting suggestion that, roughly, deformation-classes (concordance classes) of 2d SCFTs with target space $X$ are the generalized cohomology of $X$ with coefficients in the spectrum of topological modular forms (tmf):

and the more explicit suggestion that, under this identification, the Chern-Dold character from tmf to modular forms, sends a 2d SCFT to its partition function/elliptic genus/supersymmetric index:

This perspective is also picked up in Gukov, Pei, Putrov & Vafa 18.

Discussion of the 2d SCFTs (namely supersymmetric SU(2)-WZW-models) conjecturally corresponding, under this conjectural identification, to the elements of $\mathbb{Z}/24$ $\simeq$ $tmf^{-3}(\ast) = \pi_3(tmf)$ $\simeq$ $\pi_3(\mathbb{S})$ (the third stable homotopy group of spheres):

#### Occurrences in string theory

##### H-string elliptic genus

Further on the elliptic genus of the heterotic string being the Witten genus:

The interpretation of equivariant elliptic genera as partition functions of parametrized WZW models in heterotic string theory:

Speculations on physics aspects of lifting the Witten genus to topological modular forms:

##### M5-brane elliptic genus

On the M5-brane elliptic genus:

A 2d SCFT argued to describe the KK-compactification of the M5-brane on a 4-manifold (specifically: a complex surface) originates with

Discussion of the resulting elliptic genus (2d SCFT partition function) originates with:

Further discussion in:

##### M-string elliptic genus

On the elliptic genus of M-strings inside M5-branes:

##### E-string elliptic genus

On the elliptic genus of E-strings as wrapped M5-branes:

• J. A. Minahan, D. Nemeschansky, Cumrun Vafa, N. P. Warner, E-Strings and $N=4$ Topological Yang-Mills Theories, Nucl. Phys. B527 (1998) 581-623 (arXiv:hep-th/9802168)

• Wenhe Cai, Min-xin Huang, Kaiwen Sun, On the Elliptic Genus of Three E-strings and Heterotic Strings, J. High Energ. Phys. 2015, 79 (2015). (arXiv:1411.2801, doi:10.1007/JHEP01(2015)079)

Last revised on November 29, 2020 at 04:18:48. See the history of this page for a list of all contributions to it.