nLab
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

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 S 1×S 1 2S^1 \times S^1 \sslash \mathbb{Z}_2 (see also M-theory on S1/G_HW times H/G_ADE):

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 }

table from BLT 13

Properties

Tadpole cancellation and SO(32)SO(32)-GUT in Type I

For type I string theory on flat (toroidal) target spacetime orientifolds 9,1\mathbb{R}^{9,1} (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).

Tadpole cancellation and SO(16)×SO(16)SO(16) \times SO(16)-GUT in Type I’

For type I’ string theory on flat (toroidal) target spacetime orientifolds X 8,1×𝕊 1/ 2X^{8,1} \times \mathbb{S}^1/\mathbb{Z}_2 (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 32=2(16)-32 = 2 \cdot (-16) (here).

Discussion of Spin(16)-GUT phenomenology:

(…)

Orbifolds of type I

Type I’ on toroidal orientifolds with ADE-singularities (e.g. Bergman&Rodriguez-Gomez 12, Sec. 3)

dual to heterotic M-theory on ADE-orbifolds.

(…)

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’

Original articles on type I' string theory:

Type I’ on toroidal orientifolds with ADE-singularities (dual to heterotic M-theory on ADE-orbifolds):

Phenomenology

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 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

Geometric engineering of D=6D=6 𝒩=(1,0)\mathcal{N}=(1,0) SCFT

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):

Last revised on September 12, 2019 at 03:55:15. See the history of this page for a list of all contributions to it.