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What is called type I string theory is type IIB string theory on orientifold spacetimes, hence on O9-planes.
Its T-dual, called type I’ string theory, is type IIA string theory on O8-planes, which under the duality between M-theory and type IIA string theory is M-theory KK-compactified on the orientifold (see also M-theory on S1/G_HW times H/G_ADE):
table from BLT 13
For type I string theory on flat (toroidal) target spacetime orientifolds (i.e. for type IIB string theory on flat toroidal O9-planes) RR-field tadpole cancellation requires 32 D-branes (see this Remark for counting D-branes in orientifolds) to cancel the O-plane charge of -32 (here).
Under the duality between type I and heterotic string theory this translates to the semi-spin gauge group SemiSpin(32) of heterotic string theory.
Discussion of type-I string phenomenology and grand unified theory based on SO(32) type-I strings: (MMRB 86, Ibanez-Munoz-Rigolin 98, Yamatsu 17).
For type I’ string theory on flat (toroidal) target spacetime orientifolds (i.e. for type IIA string theory on two flat toroidal O8-planes) RR-field tadpole cancellation requires 16 D-branes (see this Remark for counting D-branes in orientifolds) on each of the two O8-planes to cancel the total O-plane charge of (here).
Discussion of Spin(16)-GUT phenomenology:
(…)
Type I’ on toroidal orientifolds with ADE-singularities (e.g. Bergman&Rodriguez-Gomez 12, Sec. 3)
dual to heterotic M-theory on ADE-orbifolds.
(…)
See at duality between type I and heterotic string theory
One considers the KK-compactification of M-theory on a Z/2-orbifold of a torus, hence of the Cartesian product of two circles
such that the reduction on the first factor corresponds to the duality between M-theory and type IIA string theory, hence so that subsequent T-duality along the second factor yields type IIB string theory (in its F-theory-incarnation). Now the diffeomorphism which exchanges the two circle factors and hence should be a symmetry of M-theory is interpreted as S-duality in type II string theory:
graphics taken from Horava-Witten 95, p. 15
If one considers this situation additionally with a -orbifold quotient of the first circle factor, one obtains the duality between M-theory and heterotic string theory (Horava-Witten theory). If instead one performs it on the second circle factor, one obtains type I string theory.
Here in both cases the involution action is by reflection of the circle at a line through its center. Hence if we identify then the action is by multiplication by /1 on the real line.
In summary:
M-theory on
yields heterotic string theory
yields type I' string theory
Hence the S-duality that swaps the two circle factors corresponds to a duality between heterotic E and type I’ string theory. And T-dualizing turns this into a duality between type I and heterotic string theory.
graphics taken from Horava-Witten 95, p. 16
cohomology theories of string theory fields on orientifolds
Luis Ibáñez, Angel Uranga, section 4.4.3 of: String Theory and Particle Physics – An Introduction to String Phenomenology, Cambridge University Press 2012
Ralph Blumenhagen, Dieter Lüst, Stefan Theisen, Section 9.4 and 10.6 of: Basic Concepts of String Theory Part of the series Theoretical and Mathematical Physics, Springer 2013
Relation to M-theory (via Horava-Witten theory):
Petr Hořava, Edward Witten, Heterotic and Type I string dynamics from eleven dimensions, Nucl. Phys. B460 (1996) 506 (arXiv:hep-th/9510209)
Petr Hořava, Edward Witten, Eleven dimensional supergravity on a manifold with boundary, Nucl. Phys. B475 (1996) 94 (arXiv:hep-th/9603142)
A comprehensive discussion of the (differential) cohomological nature of general type II/type I orientifold backgrounds is in
with details in
Daniel Freed, Lectures on twisted K-theory and orientifolds (pdf)
Jacques Distler, Dan Freed, Greg Moore, Spin structures and superstrings, Surveys in Differential Geometry, Volume 15 (2010) (arXiv:1007.4581, doi:10.4310/SDG.2010.v15.n1.a4)
Related lecture notes / slides include
Jacques Distler, Orientifolds and Twisted KR-Theory (2008) (pdf)
Daniel Freed, Dirac charge quantiation, K-theory, and orientifolds, talk at a workshop Mathematical methods in general relativity and quantum field theories, November, 2009 (pdf)
Greg Moore, The RR-charge of an orientifold, Oberwolfach talk 2010 (pdf, pdf, ppt)
Original articles on type I' string theory:
John Schwarz, Some Properties of Type I’ String Theory, in: Mikhail Shifman (ed.), The Many Faces of the Superworld, pp. 388-397 (2000) (arXiv:hep-th/9907061, doi:10.1142/9789812793850_0023)
Justin R. David, Avinash Dhar, Gautam Mandal, Probing Type I’ String Theory Using D0 and D4-Branes, Phys. Lett. B415 (1997) 135-143 (arXiv:hep-th/9707132)
Type I’ on toroidal orientifolds with ADE-singularities (dual to heterotic M-theory on ADE-orbifolds):
Type I string phenomenology and discussion of GUTs based on SO(32) type I strings (see also at heterotic phenomenology):
H.S. Mani, A. Mukherjee, R. Ramachandran, A.P. Balachandran, Embedding of GUT in superstring theories, Nuclear Physics B Volume 263, Issues 3–4, 27 January 1986, Pages 621-628 (arXiv:10.1016/0550-3213(86)90277-4)
Luis Ibáñez, C. Muñoz, S. Rigolin, Aspects of Type I String Phenomenology, Nucl.Phys. B553 (1999) 43-80 (arXiv:hep-ph/9812397)
Emilian Dudas, Theory and Phenomenology of Type I strings and M-theory, Class. Quant. Grav.17:R41-R116, 2000 (arXiv:hep-ph/0006190)
Naoki Yamatsu, String-Inspired Special Grand Unification, Progress of Theoretical and Experimental Physics, Volume 2017, Issue 10, 1 (arXiv:1708.02078, doi:10.1093/ptep/ptx135)
Discussion of duality with heterotic string theory includes the following.
The original conjecture is due to
More details are then in
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, 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)
Last revised on July 24, 2021 at 06:18:47. See the history of this page for a list of all contributions to it.