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type I string theory

Contents

Context

String theory

Physics

physics, mathematical physics, philosophy of physics

Surveys, textbooks and lecture notes


theory (physics), model (physics)

experiment, measurement, computable physics

Gravity

Quantum field theory

Higher spin geometry

Elliptic cohomology

Contents

Idea

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 }

Properties

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).

Dualities

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

References

General

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’

Phenomenology

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)

Duality

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.