# Type I string theory

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Aspect of theoretical physics

String theory Fundamental objects String Cosmic string Brane D-brane Perturbative theory Bosonic Superstring (Type I, Type II, Heterotic) Non-perturbative results S-duality T-duality U-duality M-theory F-theory AdS/CFT correspondence Phenomenology Phenomenology Cosmology Brane cosmology Landscape Mathematics Geometric Langlands correspondence Mirror symmetry Monstrous moonshine Vertex algebra K-theory Related concepts Theory of everything Conformal field theory Quantum gravity Supersymmetry Supergravity Twistor string theory N = 4 supersymmetric Yang–Mills theory Kaluza–Klein theory Multiverse Holographic principle Theorists Aganagić Arkani-Hamed Atiyah Banks Berenstein Bousso Costello Curtright Dijkgraaf Distler Douglas Duff Dvali Ferrara Fischler Friedan Gates Gliozzi Gopakumar Green Greene Gross Gubser Gukov Guth Hanson Harvey Hořava Horowitz Gibbons Kachru Kaku Kallosh Kaluza Kapustin Klebanov Knizhnik Kontsevich Klein Linde Maldacena Mandelstam Marolf Martinec Minwalla Moore Motl Mukhi Myers Nanopoulos Năstase Nekrasov Neveu Nielsen van Nieuwenhuizen Novikov Olive Ooguri Ovrut Polchinski Polyakov Rajaraman Ramond Randall Randjbar-Daemi Roček Rohm Sagnotti Scherk Schwarz Seiberg Sen Shenker Siegel Silverstein Sơn Staudacher Steinhardt Strominger Sundrum Susskind 't Hooft Townsend Trivedi Turok Vafa Veneziano Verlinde Verlinde Wess Witten Yau Yoneya Zamolodchikov Zamolodchikov Zaslow Zumino Zwiebach History Glossary v t e

In [theoretical physics](/source/Theoretical_physics), **type I string theory** is one of five consistent supersymmetric [string theories](/source/String_theory) in ten dimensions. It is the only one whose strings are unoriented[1] (both orientations of a string are equivalent) and the only one which perturbatively contains not only [closed strings](/source/Closed_string), but also [open strings](/source/Open_string_(physics)). The terminology of type I and [type II](/source/Type_II_string_theory) was coined by [John Henry Schwarz](/source/John_Henry_Schwarz) in 1982 to classify the three string theories known at the time.[2]

## Overview

The classic 1976 work of [Ferdinando Gliozzi](/source/Ferdinando_Gliozzi), [Joël Scherk](/source/Jo%C3%ABl_Scherk) and [David Olive](/source/David_Olive)[3] paved the way to a systematic understanding of the rules behind string spectra in cases where only [closed strings](/source/Closed_string) are present via [modular invariance](/source/Modular_invariance). It did not lead to similar progress for models with open strings, despite the fact that the original discussion was based on the type I string theory.

As first proposed by [Augusto Sagnotti](/source/Augusto_Sagnotti) in 1988,[4] the type I string theory can be obtained as an [orientifold](/source/Orientifold) of [type IIB string](/source/Type_IIB_string) theory, with 32 half-[D9-branes](/source/D9-brane) added in the vacuum to cancel various [anomalies](/source/Anomaly_(physics)) giving it a gauge group of SO(32) via [Chan–Paton factors](/source/Chan%E2%80%93Paton_factor).

At low energies, type I string theory is described by the [type I supergravity](/source/Type_I_supergravity) in ten dimensions coupled to the SO(32) [supersymmetric](/source/Supersymmetric) [Yang–Mills theory](/source/Yang%E2%80%93Mills_theory). The discovery in 1984 by [Michael Green](/source/Michael_Green_(physicist)) and John H. Schwarz that anomalies in type I string theory cancel sparked the [first superstring revolution](/source/First_superstring_revolution). However, a key property of these models, shown by A. Sagnotti in 1992, is that in general the Green–Schwarz mechanism takes a more general form, and involves several two forms in the cancellation mechanism.

The relation between the [type IIB](/source/Type_II_string_theory#Type_IIB_string_theory) string theory and the type I string theory has a large number of surprising consequences, both in ten and in lower dimensions, that were first displayed by the String Theory Group at the [University of Rome Tor Vergata](/source/University_of_Rome_Tor_Vergata) in the early 1990s. It opened the way to the construction of entire new classes of string spectra with or without supersymmetry. [Joseph Polchinski](/source/Joseph_Polchinski)'s work on D-branes provided a geometrical interpretation for these results in terms of extended objects ([D-brane](/source/D-brane), [orientifold](/source/Orientifold)).

In the 1990s it was first argued by [Edward Witten](/source/Edward_Witten) that type I string theory with the string coupling constant g {\displaystyle g} is equivalent to the SO(32) [heterotic string](/source/Heterotic_string) with the coupling 1 / g {\displaystyle 1/g} . This equivalence is known as [S-duality](/source/S-duality).

## Notes

1. **[^](#cite_ref-1)** Tzitzimpasis, P.[https://webspace.science.uu.nl/~caval101/homepage/Students_files/TzitzimpasisMaster.pdf](https://webspace.science.uu.nl/~caval101/homepage/Students_files/TzitzimpasisMaster.pdf)

1. **[^](#cite_ref-2)** [Schwarz, J.H.](/source/John_Henry_Schwarz) (1982). ["Superstring theory"](https://dx.doi.org/10.1016/0370-1573%2882%2990087-4). *Physics Reports*. **89** (3): 223–322. [Bibcode](/source/Bibcode_(identifier)):[1982PhR....89..223S](https://ui.adsabs.harvard.edu/abs/1982PhR....89..223S). [doi](/source/Doi_(identifier)):[10.1016/0370-1573(82)90087-4](https://doi.org/10.1016%2F0370-1573%2882%2990087-4).

1. **[^](#cite_ref-3)** F. Gliozzi, J. Scherk and D. I. Olive, "Supersymmetry, Supergravity Theories and the Dual Spinor Model", *Nucl. Phys. B* **122** (1977), 253.

1. **[^](#cite_ref-4)** Sagnotti, A. (1988). "Open strings and their symmetry groups". In 't Hooft, G.; Jaffe, A.; Mack, G.; Mitter, P. K.; Stora, R. (eds.). *Nonperturbative Quantum Field Theory*. [Plenum Publishing Corporation](/source/Plenum_Publishing_Corporation). pp. 521–528. [arXiv](/source/ArXiv_(identifier)):[hep-th/0208020](https://arxiv.org/abs/hep-th/0208020). [Bibcode](/source/Bibcode_(identifier)):[2002hep.th....8020S](https://ui.adsabs.harvard.edu/abs/2002hep.th....8020S).

## References

- E. Witten, "String theory dynamics in various dimensions", *Nucl. Phys. B* **443** (1995) 85. [arXiv:hep-th/9503124](https://arxiv.org/abs/hep-th/9503124).

- J. Polchinski, S. Chaudhuri and C.V. Johnson, "Notes on D-Branes", [arXiv:hep-th/9602052](https://arxiv.org/abs/hep-th/9602052).

- C. Angelantonj and A. Sagnotti, "Open strings", *Phys. Rep.* **1** [(Erratum-ibid.) 339] [arXiv:hep-th/0204089](https://arxiv.org/abs/hep-th/0204089).

v t e String theory Background Strings Cosmic strings History of string theory First superstring revolution Second superstring revolution String theory landscape Theory Nambu–Goto action Polyakov action Bosonic string theory Superstring theory Type I string Type II string Type IIA string Type IIB string Heterotic string N=2 superstring F-theory String field theory Matrix string theory Non-critical string theory Non-linear sigma model Tachyon condensation RNS formalism GS formalism String duality T-duality S-duality U-duality Montonen–Olive duality Particles and fields Graviton Dilaton Tachyon Ramond–Ramond field Kalb–Ramond field Magnetic monopole Dual graviton Dual photon Branes D-brane NS5-brane M2-brane M5-brane S-brane Black brane Black holes Black string Brane cosmology Quiver diagram Hanany–Witten transition Conformal field theory Virasoro algebra Mirror symmetry Conformal anomaly Conformal algebra Superconformal algebra Vertex operator algebra Loop algebra Kac–Moody algebra Wess–Zumino–Witten model Gauge theory Anomalies Instantons Chern–Simons form Bogomol'nyi–Prasad–Sommerfield bound Exceptional Lie groups (G2, F4, E6, E7, E8) ADE classification Dirac string p-form electrodynamics Geometry Worldsheet Kaluza–Klein theory Compactification Why 10 dimensions? Kähler manifold Ricci-flat manifold Calabi–Yau manifold Hyperkähler manifold K3 surface G2 manifold Spin(7)-manifold Generalized complex manifold Orbifold Conifold Orientifold Moduli space Hořava–Witten theory K-theory (physics) Twisted K-theory Supersymmetry Supergravity Eleven-dimensional supergravity Type I supergravity Type IIA supergravity Type IIB supergravity Superspace Lie superalgebra Lie supergroup Holography Holographic principle AdS/CFT correspondence M-theory Matrix theory Introduction to M-theory String theorists Aganagić Arkani-Hamed Atiyah Banks Berenstein Bousso Curtright Dijkgraaf Distler Douglas Duff Dvali Ferrara Fischler Friedan Gates Gliozzi Gopakumar Green Greene Gross Gubser Gukov Guth Hanson Harvey 't Hooft Hořava Gibbons Kachru Kaku Kallosh Kaluza Kapustin Klebanov Knizhnik Kontsevich Klein Linde Maldacena Mandelstam Marolf Martinec Minwalla Moore Motl Mukhi Myers Nanopoulos Năstase Nekrasov Neveu Nielsen van Nieuwenhuizen Novikov Olive Ooguri Ovrut Polchinski Polyakov Rajaraman Ramond Randall Randjbar-Daemi Roček Rohm Sagnotti Scherk Schwarz Seiberg Sen Shenker Siegel Silverstein Sơn Staudacher Steinhardt Strominger Sundrum Susskind Townsend Trivedi Turok Vafa Veneziano Verlinde Verlinde Wess Witten Yau Yoneya Zamolodchikov Zamolodchikov Zaslow Zumino Zwiebach

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