The KK-compactification of M-theory on fibers
which are, locally, the Cartesian product of
the circle orientifolded by as in Horava-Witten theory;
the quaternions orbifolded by a finite subgroup of SU(2) .
(Sen 97, Sec 3, Faux-Lüst-Ovrut 99, Kaplunovsky-Sonnenschein-Theisen-Yankielowicz 99, Faux-Lüst-Ovrut 00a, 00b, 00c)
graphics grabbed from HSS18, Example 2.2.7
For this subsumes M-theory on K3 times (Seiberg-Witten 96)
Under duality in string theory (specifically: duality between M-theory and type IIA string theory and duality between M-theory and heterotic string theory) M-theory on appears through the following string theory-perspectives
The following graphics shows how the three perspectives arise from KK-compactification on three different choices of circle-fibers. Indicated also are the M5-branes and their string theoretic images at NS5-branes/D4-branes with geometrically engineer D=6 N=(1,0) SCFTs (see further below).
graphics grabbed from SS19
(…)
Horava-Witten theory, hence heterotic string theory, on ADE-singularities
(Witten 99,…)
(…)
from GKSTY 02
If in addition the black NS5-brane sits at an O8-plane, hence at the orientifold fixed point-locus, then in the ordinary -quotient it appears as a “half-brane” – the half M5-brane – with only one copy of D6-branes ending on it:
graphics grabbed from GKSTY 02
(In Hanany-Zaffaroni 99 this is interpreted in terms of the 't Hooft-Polyakov monopole.)
The lift to M-theory of this situation is an M5-brane intersecting an M9-brane (see at M-theory on S1/G_HW times H/G_ADE):
from GKSTY 02
Alternatively the O8-plane may intersect the black D6-branes away from the black NS5-brane:
from HKLY 15
In general, some of the NS5 sit away from the O8-plane, while some sit on top of it:
from Hanany-Zaffaroni 98
(Bergman & Rodriguez-Gomez 12, Sec. 3)
(…)
The M5-branes-configurations as above are supposed to geometrically engineer D=6 N=(1,0) SCFTs.
See the references below, for example DHTV 14, Section 6, Gaiotto-Tomasiello 14, HKLY 15.
The first discussion of this compactification is possibly
in the context of the M-theory lift of gauge enhancement on D6-branes.
The original articles focusing on this situation:
Michael Faux, Dieter Lüst, Burt Ovrut, Intersecting Orbifold Planes and Local Anomaly Cancellation in M-Theory, Nucl. Phys. B554: 437-483, 1999 (arXiv:hep-th/9903028)
Michael Faux, Dieter Lüst, Burt Ovrut, Local Anomaly Cancellation, M-Theory Orbifolds and Phase-Transitions, Nucl. Phys. B589: 269-291, 2000 (arXiv:hep-th/0005251)
Michael Faux, Dieter Lüst, Burt Ovrut, An M-Theory Perspective on Heterotic K3 Orbifold Compactifications, Int. J. Mod. Phys. A18:3273-3314, 2003 (arXiv:hep-th/0010087)
Michael Faux, Dieter Lüst, Burt Ovrut, Twisted Sectors and Chern-Simons Terms in M-Theory Orbifolds, Int. J. Mod. Phys. A18: 2995-3014, 2003 (arXiv:hep-th/0011031)
Vadim Kaplunovsky, Jacob Sonnenschein, Stefan Theisen, Shimon Yankielowicz, On the Duality between Perturbative Heterotic Orbifolds and M-Theory on , Nuclear Physics B Volume 590, Issues 1–2, 4 December 2000, Pages 123-160 Nuclear Physics B (arXiv:hep-th/9912144, doi:10.1016/S0550-3213(00)00460-0)
E. Gorbatov, Vadim Kaplunovsky, Jacob Sonnenschein, Stefan Theisen, Shimon Yankielowicz, On Heterotic Orbifolds, M Theory and Type I’ Brane Engineering, JHEP 0205:015 (2002) [arXiv:hep-th/0108135, doi:10.1088/1126-6708/2002/05/015]
Discussion of heterotic M-theory on smooth K3 originates around
Nathan Seiberg, Edward Witten, Comments on String Dynamics in Six Dimensions, Nucl. Phys. B471:121-134, 1996 (arXiv:hep-th/9603003)
Zygmunt Lalak, Steven Thomas, Gaugino Condensation, Moduli Potentials and Supersymmetry Breaking in M-Theory Models, Nuclear Physics B Volume 515, Issues 1–2, 30 March 1998, Pages 55-72 Nuclear Physics B (hep-th/9707223, doi:10.1016/S0550-3213(97)00784-0)
(on gaugino condensation)
See also
Jacob Cole Claussen, The deconstruction of orbifold fixed points in heterotic M-theory, 2016 (hdl:2152/41748)
John Huerta, Hisham Sati, Urs Schreiber, Example 2.2.7 of: Real ADE-equivariant (co)homotopy and Super M-branes, CMP (2019) (arXiv:1805.05987, doi:10.1007/s00220-019-03442-3)
Domenico Fiorenza, Hisham Sati, Urs Schreiber, Section 4 of: Super-exceptional geometry: origin of heterotic M-theory and super-exceptional embedding construction of M5 (arXiv:1908.00042)
Hisham Sati, Urs Schreiber, Section 4.1 of: Equivariant Cohomotopy implies orientifold tadpole cancellation (arXiv:1909.12277)
As heterotic string theory on orbifold ADE-singularities:
As type I' string theory with D6-branes:
Ilka Brunner, Andreas Karch, Branes at Orbifolds versus Hanany Witten in Six Dimensions, JHEP 9803:003, 1998 (arXiv:hep-th/9712143)
Amihay Hanany, Alberto Zaffaroni, Branes and Six Dimensional Supersymmetric Theories, Nucl.Phys. B529 (1998) 180-206 (arXiv:hep-th/9712145)
Amihay Hanany, Alberto Zaffaroni, Monopoles in String Theory, JHEP 9912 (1999) 014 (arXiv:hep-th/9911113)
Hirotaka Hayashi, Sung-Soo Kim, Kimyeong Lee, Masato Taki, Futoshi Yagi, A new 5d description of 6d D-type minimal conformal matter, JHEP 1508:097, 2015 (arXiv:1505.04439)
Ibrahima Bah, Achilleas Passias, Alessandro Tomasiello, compactifications with punctures in massive IIA supergravity, JHEP11 (2017)050 (arXiv:1704.07389)
and in massive type IIA string theory with D6-D8 brane bound states:
As type I' string theory at orbifold ADE-singularities:
Oren Bergman, Diego Rodriguez-Gomez, Section 3 of: 5d quivers and their duals, JHEP07 (2012) 171 (arxiv:1206.3503)
Chiung Hwang, Joonho Kim, Seok Kim, Jaemo Park, Section 3.4.2 of: General instanton counting and 5d SCFT, JHEP07 (2015) 063 (arxiv:1406.6793)
The F-theory perspective:
Monika Marquart, Daniel Waldram, F-theory duals of M-theory on (arXiv:hep-th/0204228)
Christoph Lüdeling, Fabian Ruehle, F-theory duals of singular heterotic K3 models, Phys. Rev. D 91, 026010 (2015) (arXiv:1405.2928)
On D=6 N=(1,0) SCFTs via geometric engineering on M5-branes/NS5-branes at D-, E-type ADE-singularities, notably from M-theory on S1/G_HW times H/G_ADE, hence from orbifolds of type I' string theory (see at half NS5-brane):
Michele Del Zotto, Jonathan Heckman, Alessandro Tomasiello, Cumrun Vafa, Section 6 of: 6d Conformal Matter, JHEP02(2015)054 (arXiv:1407.6359)
Davide Gaiotto, Alessandro Tomasiello, Holography for theories in six dimensions, JHEP12(2014)003 (arXiv:1404.0711)
Kantaro Ohmori, Hiroyuki Shimizu, Compactifications of 6d Theories and Brane Webs, J. High Energ. Phys. (2016) 2016: 24 (arXiv:1509.03195)
Hirotaka Hayashi, Sung-Soo Kim, Kimyeong Lee, Futoshi Yagi, 6d SCFTs, 5d Dualities and Tao Web Diagrams, JHEP05 (2019)203 (arXiv:1509.03300)
Ibrahima Bah, Achilleas Passias, Alessandro Tomasiello, compactifications with punctures in massive IIA supergravity, JHEP11 (2017)050 (arXiv:1704.07389)
Santiago Cabrera, Amihay Hanany, Marcus Sperling, Magnetic Quivers, Higgs Branches, and 6d Theories, J. High Energ. Phys. (2019) 2019: 71 (arXiv:1904.12293)
Emergence of SU(2) flavor-symmetry on single M5-branes in heterotic M-theory on ADE-orbifolds (in the D=6 N=(1,0) SCFT on small instantons in heterotic string theory):
Abhijit Gadde, Babak Haghighat, Joonho Kim, Seok Kim, Guglielmo Lockhart, Cumrun Vafa, Section 4.2 of: 6d String Chains, J. High Energ. Phys. 2018, 143 (2018) (arXiv:1504.04614, doi:10.1007/JHEP02(2018)143)
Kantaro Ohmori, Section 2.3.1 of: Six-Dimensional Superconformal Field Theories and Their Torus Compactifications, Springer Theses 2018 (springer:book/9789811330919)
Argument for this by translation under duality between M-theory and type IIA string theory to half NS5-brane/D6/D8-brane bound state systems in type I' string theory:
Reviewed in:
The emergence of flavor in these half NS5-brane/D6/D8-brane bound state systems, due to the semi-infinite extension of the D6-branes making them act as flavor branes:
Amihay Hanany, Alberto Zaffaroni, Branes and Six Dimensional Supersymmetric Theories, Nucl.Phys. B529 (1998) 180-206 (arXiv:hep-th/9712145)
Ilka Brunner, Andreas Karch, Branes at Orbifolds versus Hanany Witten in Six Dimensions, JHEP 9803:003, 1998 (arXiv:hep-th/9712143)
Reviewed in:
See also:
Last revised on September 24, 2024 at 06:46:21. See the history of this page for a list of all contributions to it.