nLab E-string




In string theory, specifically in type IIA string theory, the brane intersection of a D2-brane with an O8-plane is called an E-string.

graphics grabbed from KKLPV 14, p. 4

Hence under the S-duality between type I and heterotic string theory the E-string is dual to the heterotic string.

The M-theory lift of the E-string is the brane intersection of an M2-brane with an M9-brane which wraps the M-theory circle fiber, hence an M9 IM9_I-brane of Horava-Witten theory (KKLPV 14, p. 4/5), hence a D8-brane from the dual perspective of type I' string theory.

The other end of the M2-brane-lift of the E-string is on an M5-brane:

graphics grabbed from GHKKLV 15

graphics grabbed from HLV 14

In contrast, if both ends of the M2-brane are on an M5-brane, some authors speak of “M-strings”:

graphics grabbed from HLV 14

Finally, an M2-brane stretching between two MO9-planes gives the heterotic string at its boundary:

from Kashima 00


E-string elliptic genus

See at E-string elliptic genus.

KK-compactification of M-theory

brane intersections/bound states/wrapped branes/polarized branes

S-duality\,bound states:




E-strings as M5-branes wrapped on a half K3?:

E-strings as M2-branes stretched between M5 and MO9:

On their Seiberg-Witten curve:

and on their quantum Seiberg-Witten curve in relation to D6-D8-brane bound states:

On the E-string elliptic genus:

On the Green-Schwarz anomaly cancellation in D=6 N=(1,0) SCFT:

See also:

  • Sung-Soo Kim, Yuji Sugimoto, Futoshi Yagi, Surface defects on E-string from 5-brane webs, JHEP 12(2020) 183 (arXiv:2008.06428)

In F-theory

Discussion in F-theory:

  • Jie Gu, Babak Haghighat, Albrecht Klemm, Kaiwen Sun, Xin Wang, Elliptic Blowup Equations for 6d SCFTs. III: E–strings, M–strings and Chains (arXiv:1911.11724)

In heterotic M-theory on ADE-orbifolds

Discussion in heterotic M-theory on ADE-orbifolds, where the M5-branes parallel to an MO9 sit on an MK6/D6-brane on an ADE-singularity:

Relation to Dpp-D(p+2)(p+2)-brane bound states

The lift of Dp-D(p+2)-brane bound states in string theory to M2-M5-brane bound states/E-strings in M-theory, under duality between M-theory and type IIA string theory+T-duality, via generalization of Nahm's equation (eventually motivating the BLG model/ABJM model):

Last revised on January 8, 2024 at 08:07:57. See the history of this page for a list of all contributions to it.