nLab
E-string

Idea

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 $M9_I$-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

Related concepts

KK-compactification of M-theory

• M-theory on a circle

• M-theory on Spin(7)-manifolds

• M-theory on G2-manifolds

  • G2-MSSM

• M-theory on Sp(1)-manifolds

• M-theory on hyperbolic manifolds

• M-theory on S1/G_HW times H/G_ADE (heterotic M-theory on ADE-orbifolds)

• M-theory on Calabi-Yau manifolds

  • F/M-theory on elliptically fibered Calabi-Yau 3-folds

  • F/M-theory on elliptically fibered Calabi-Yau 4-folds

brane intersections/bound states/wrapped branes

• D-branes and anti D-branes form bound states by tachyon condensation, thought to imply the classification of D-brane charge by K-theory

• intersecting D-branes/fuzzy funnels:

  • Dp-D(p+2)-brane bound state and Yang-Mills monopoles

    • D0-D2 brane bound state

    • D1-D3 brane bound state

    • D2-D4 brane bound state

    • D3-D5 brane bound state

    • D4-D6 brane bound state

    • D6-D8-brane bound state

  • Dp-D(p+4)-brane bound state and Yang-Mills instantons

    • D0-D4 brane bound state

    • D1-D5 brane bound state

    • D2-D6 brane bound state

    • D3-D7 brane bound state

    • D4-D8 brane bound state

    • D5-D9 brane bound state

      small instanton

• Dp-D(p+6) brane bound state

  • D0-D6 brane bound state

  • D1-D7 brane bound state

  • D2-D8 brane bound state

• NS5-D4-D2 bound states

S-duality$\,$bound states:

• (p,q)-string

• (p,q)5-branes

• string network

• 5-brane web

intersecting$\,$M-branes:

• M5-MO9 brane bound state

• M2-M5 brane bound states

• E-strings

• membrane triple junction

References

General

• Babak Haghighat, Guglielmo Lockhart, Cumrun Vafa, Fusing E-string to heterotic string: $E + E \to H$, Phys. Rev. D 90, 126012 (2014) (arXiv:1406.0850)

• Joonho Kim, Seok Kim, Kimyeong Lee, Jaemo Park, Cumrun Vafa, Elliptic Genus of E-strings, JHEP 1709 (2017) 098 (arXiv:1411.2324)

• Abhijit Gadde, Babak Haghighat, Joonho Kim, Seok Kim, Guglielmo Lockhart, Cumrun Vafa, 6d String Chains, JHEP 1802 (2018) 143 (arXiv:1504.04614)

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)

Relation to D$p$-D$(p+2)$-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):

• Anirban Basu, Jeffrey Harvey, The M2-M5 Brane System and a Generalized Nahm’s Equation, Nucl.Phys. B713 (2005) 136-150 (arXiv:hep-th/0412310)

• Jonathan Bagger, Neil Lambert, Sunil Mukhi, Constantinos Papageorgakis, Section 2.2.1 of Multiple Membranes in M-theory, Physics Reports, Volume 527, Issue 1, 1 June 2013, Pages 1-100 (arXiv:1203.3546, doi:10.1016/j.physrep.2013.01.006)