String theory


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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.


M-string elliptic genus

See at M-string elliptic genus.

brane intersections/bound states/wrapped branes/polarized branes

S-duality\,bound states:




Elliptic genera as super pp-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 – originates with:

Review in:

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 functorial QFT

Tentative formulation via functorial quantum field theory ((2,1)-dimensional Euclidean field theories and tmf):

Via conformal nets

Tentative formulation via conformal nets:

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:

On the elliptic genus of E-strings as M2-branes ending on M5-branes:

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