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Heterotic string theory

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Physics concept of subatomic structure

This article is about string theory. For heterosis in biology, seeHeterosis.

String theory

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Instring theory, aheterotic string is a closed string (or loop) which is a hybrid ('heterotic') of asuperstring and abosonic string. There are two kinds of heterotic superstring theories, the heterotic SO(32) and the heterotic E₈ × E₈, abbreviated toHO andHE. Apart from that there exist seven more heterotic string theories which are notsupersymmetric and hence are only of secondary importance in most applications.^[1] Heterotic string theory was first developed in 1985 byDavid Gross,Jeffrey Harvey,Emil Martinec, andRyan Rohm^[2] (the so-called "Princeton string quartet"^[3]), in one of the key papers that fueled thefirst superstring revolution.

Overview

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Instring theory, the left-moving and the right-moving excitations of strings are completely decoupled for a closed string,^[4] and it is possible to construct a string theory whose left-moving (counter-clockwise) excitations are treated as a bosonic string propagating inD = 26 dimensions, while the right-moving (clockwise) excitations are treated as a superstring inD = 10 dimensions.

The mismatched 16 dimensions must be compactified on an even,self-dual lattice (adiscrete subgroup of a linear space). There are two possible even self-dual lattices in 16 dimensions, and it leads to two types of the heterotic string. They differ by thegauge group in 10 dimensions. One gauge group isSO(32) (the HO string) while the other isE₈ × E₈ (the HE string).^[5]

These two gauge groups also turned out to be the only twoanomaly-free gauge groups that can be coupled to theN = 1 supergravity in 10 dimensions. (Although not realized for quite some time, U(1)⁴⁹⁶ and E₈ × U(1)²⁴⁸ are anomalous.^[6])

Every heterotic string must be aclosed string, not anopen string; it is not possible to define anyboundary conditions that would relate the left-moving and the right-moving excitations because they have a different character.

String duality

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String duality is a class of symmetries in physics that link different string theories. In the 1990s, it was realized that the strong coupling limit of the HO theory istype I string theory — a theory that also containsopen strings; this relation is calledS-duality. The HO and HE theories are also related byT-duality.

Because the various superstring theories were shown to be related by dualities, it was proposed that each type of string was a different limit of a single underlying theory calledM-theory.

References

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^Polchinski, Joseph (1998).String Theory: Superstring Theory and Beyond. Vol. 2. Cambridge University Press. pp. 55–59.ISBN 9780521633048.
^Gross, David J.; Harvey, Jeffrey A.; Martinec, Emil; Rohm, Ryan (1985-02-11). "Heterotic String".Physical Review Letters.54 (6). American Physical Society (APS):502–505.Bibcode:1985PhRvL..54..502G.doi:10.1103/physrevlett.54.502.ISSN 0031-9007.PMID 10031535.
^Dennis Overbye (2004-12-07)."String theory, at 20, explains it all (or not)".The New York Times. Retrieved2020-03-15.
^Becker, Katrin; Becker, M.; Schwarz, J. H. (2007).String theory and M-theory : a modern introduction. Cambridge New York: Cambridge University Press. p. 253.ISBN 978-0-521-86069-7.OCLC 607562796.
^Joseph Polchinski (1998).String Theory: Volume 2, p. 45.
^Adams, Allan; Taylor, Washington; DeWolfe, Oliver (2010-08-10). "String Universality in Ten Dimensions".Physical Review Letters.105 (7): 071601.arXiv:1006.1352.Bibcode:2010PhRvL.105g1601A.doi:10.1103/physrevlett.105.071601.ISSN 0031-9007.PMID 20868028.S2CID 13916249.

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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