type I string theory



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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 S 1×S 1 2S^1 \times S^1 \sslash \mathbb{Z}_2

M S 1×S 1/ 2 I T I \array{ M \\ {}^{ \mathllap{S^1 \times S^1/\mathbb{Z}_2 }}\big\downarrow \\ I' &\underset{T}{\leftrightarrow}& I }


Tadpole cancellation and SO(32)SO(32)-GUT

For type I string theory on flat (toroidal) target spacetime orientifolds 9,1\mathbb{R}^{9,1} RR-field tadpole cancellation requires 32 D-branes 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).


String-string dualities

See at duality between type I and heterotic string theory

Horava-Witten 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

S A 1 × S B 1 radius: R 11 R 10 \array{ & S^1_A &\times& S^1_B \\ \text{radius}: & R_{11} && R_{10} }

such that the reduction on the first factor S A 1S^1_A 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:

IIBSIIB IIB \overset{S}{\leftrightarrow} IIB

graphics taken from Horava-Witten 95, p. 15

If one considers this situation additionally with a /2\mathbb{Z}/2\mathbb{Z}-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 S 1/S^1 \simeq \mathbb{R} / \mathbb{Z} then the action is by multiplication by /1 on the real line.

In summary:

M-theory on

Hence the S-duality that swaps the two circle factors corresponds to duality between type I and heterotic string theory.

HE KK/ 2 A M KK/ 2 B I T T HO ASA I \array{ HE &\overset{KK/\mathbb{Z}^A_2}{\leftrightarrow}& M &\overset{KK/\mathbb{Z}^B_2}{\leftrightarrow}& I' \\ \mathllap{T}\updownarrow && && \updownarrow \mathrlap{T} \\ HO && \underset{\phantom{A}S\phantom{A}}{\leftrightarrow} && I }

graphics taken from Horava-Witten 95, p. 16

cohomology theories of string theory fields on orientifolds

string theoryB-fieldBB-field moduliRR-field
bosonic stringline 2-bundleordinary cohomology H 3H\mathbb{Z}^3
type II superstringsuper line 2-bundlePic(KU)// 2Pic(KU)//\mathbb{Z}_2KR-theory KR KR^\bullet
type IIA superstringsuper line 2-bundleBGL 1(KU)B GL_1(KU)KU-theory KU 1KU^1
type IIB superstringsuper line 2-bundleBGL 1(KU)B GL_1(KU)KU-theory KU 0KU^0
type I superstringsuper line 2-bundlePic(KU)// 2Pic(KU)//\mathbb{Z}_2KO-theory KOKO
type I˜\tilde I superstringsuper line 2-bundlePic(KU)// 2Pic(KU)//\mathbb{Z}_2KSC-theory KSCKSC



Relation to M-theory (via Horava-Witten theory):

A comprehensive discussion of the (differential) cohomological nature of general type II/type I orientifold backgrounds is in

with details in

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)

Type I’


Type I string phenomenology and discussion of GUTs based on SO(32) type I strings:

  • H.S. Mani, A. Mukherjee, R. Ramachandran, A.P. Balachandran, Embedding of SU(5)SU(5) GUT in SO(32)SO(32) 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

Last revised on July 1, 2019 at 14:59:56. See the history of this page for a list of all contributions to it.