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
Finally, an M2-brane stretching between two MO9-planes gives the heterotic string at its boundary:
from Kashima 00
See at E-string elliptic genus.
brane intersections/bound states/wrapped branes/polarized 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+6) brane bound state
intersecting$\,$M-branes:
E-strings as M5-branes wrapped on a half K3?:
J. A. Minahan, D. Nemeschansky, Nicholas Warner, Partition Functions for BPS States of the Non-Critical $E_8$ String, Adv. Theor. Math. Phys.1:167-183, 1998 (arXiv:hep-th/9707149)
J. A. Minahan, D. Nemeschansky, Cumrun Vafa, Nicholas Warner, E-Strings and $N=4$ Topological Yang-Mills Theories, Nucl. Phys. B527 (1998) 581-623 (arXiv:hep-th/9802168)
Amer Iqbal, A note on E-strings, Adv. Theor. Math. Phys. 7 (2003) 1-23 (arXiv:hep-th/0206064)
E-strings as M2-branes stretched between M5 and MO9:
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, doi:10.1103/PhysRevD.90.126012]
Abhijit Gadde, Babak Haghighat, Joonho Kim, Seok Kim, Guglielmo Lockhart, Cumrun Vafa, 6d String Chains, JHEP 1802 (2018) 143 (arXiv:1504.04614)
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:
Kenji Mohri, Exceptional String: Instanton Expansions and Seiberg-Witten Curve, Rev. Math. Phys. 14 (2002) 913-975 (arXiv:hep-th/0110121)
Joonho Kim, Seok Kim, Kimyeong Lee, Jaemo Park, Cumrun Vafa, Elliptic Genus of E-strings, JHEP 1709 (2017) 098 (arXiv:1411.2324)
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)
On the Green-Schwarz anomaly cancellation in D=6 N=(1,0) SCFT:
See also:
Discussion in F-theory:
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:
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)
Last revised on January 8, 2024 at 08:07:57. See the history of this page for a list of all contributions to it.