Type I string theory
Encyclopedia
In theoretical physics
, type I string theory is one of five consistent supersymmetric string theories
in ten dimensions. It is the only one whose strings are unoriented (both orientations of a string are equivalent) and which contains not only closed strings, but also open strings.
The classic 1976 work of Ferdinando Gliozzi, Joel Scherk
and David Olive
paved the way to a systematic understanding of the rules behind string spectra in cases where only closed strings are present via modular invariance
but did not lead to similar progress for models with closed strings, despite the fact that the original discussion was based on the type I string theory.
As first proposed by Augusto Sagnotti in 1987, the type I string theory can be obtained as an orientifold
of type IIB string theory, with 32 half-D9-branes added in the vacuum to cancel various anomalies
.
At low energies, type I string theory is described by the N=1 supergravity
(type I supergravity) in ten dimensions coupled to the SO(32) supersymmetric Yang-Mills theory. The discovery in 1984 by Michael Green
and John H. Schwarz that anomalies in type I string theory cancel sparked the 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 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" in the early Nineties. It opened the way to the construction of entire new classes of string spectra with or without supersymmetry. Joseph Polchinski
's work on D-branes provided a geometrical interpretation for these results in terms of extended objects (D brane, orientifold
).
In the 1990s it was first argued by Edward Witten
that type I string theory with the string coupling constant
is equivalent to the SO(32) heterotic string
with the coupling
. This equivalence is known as S-duality
.
References
[1] F. Gliozzi, J. Scherk and D.I. Olive, ``Supersymmetry, Supergravity Theories And The Dual Spinor Model, Nucl. Phys. B122 (1977) 253.
[2] E. Witten, ``String theory dynamics in various dimensions, Nucl. Phys. B443 (1995) 85 [arXiv:hep-th/9503124].
[3] J. Polchinski, S. Chaudhuri and C.V. Johnson, ``Notes on D-Branes, arXiv:hep-th/9602052.
[4] C. Angelantonj and A. Sagnotti, ``Open strings, Phys. Rept. 1 [Erratum-ibid. ) 339] [arXiv:hep-th/0204089].
Theoretical physics
Theoretical physics is a branch of physics which employs mathematical models and abstractions of physics to rationalize, explain and predict natural phenomena...
, type I string theory is one of five consistent supersymmetric string theories
String theory
String theory is an active research framework in particle physics that attempts to reconcile quantum mechanics and general relativity. It is a contender for a theory of everything , a manner of describing the known fundamental forces and matter in a mathematically complete system...
in ten dimensions. It is the only one whose strings are unoriented (both orientations of a string are equivalent) and which contains not only closed strings, but also open strings.
The classic 1976 work of Ferdinando Gliozzi, Joel Scherk
Joël Scherk
Joël Scherk was a French theoretical physicist who studied string theory and supergravity. Together with John H. Schwarz, he figured out that string theory was a theory of quantum gravity in 1974...
and David Olive
David Olive
David Olive CBE FLSW FRS, is a British theoretical physicist. Olive made fundamental contributions to the string theory and duality theory. He was Professor of physics at Imperial College, London...
paved the way to a systematic understanding of the rules behind string spectra in cases where only closed strings are present via modular invariance
Modular invariance
In theoretical physics, modular invariance is the invariance under the group such as SL of large diffeomorphisms of the torus. The name comes from the classical name modular group of this group, as in modular form theory....
but did not lead to similar progress for models with closed strings, despite the fact that the original discussion was based on the type I string theory.
As first proposed by Augusto Sagnotti in 1987, the type I string theory can be obtained as an orientifold
Orientifold
In theoretical physics orientifold is a generalization of the notion of orbifold, proposed by Augusto Sagnotti in 1987. The novelty is that in the case of string theory the non-trivial element of the orbifold group includes the reversal of the orientation of the string...
of type IIB string theory, with 32 half-D9-branes added in the vacuum to cancel various anomalies
Anomaly (physics)
In quantum physics an anomaly or quantum anomaly is the failure of a symmetry of a theory's classical action to be a symmetry of any regularization of the full quantum theory. In classical physics an anomaly is the failure of a symmetry to be restored in the limit in which the symmetry-breaking...
.
At low energies, type I string theory is described by the N=1 supergravity
Supergravity
In theoretical physics, supergravity is a field theory that combines the principles of supersymmetry and general relativity. Together, these imply that, in supergravity, the supersymmetry is a local symmetry...
(type I supergravity) in ten dimensions coupled to the SO(32) supersymmetric Yang-Mills theory. The discovery in 1984 by Michael Green
Michael Green (physicist)
Michael Boris Green FRS is a British physicist and one of the pioneers of string theory. Currently a professor in the Department of Applied Mathematics and Theoretical Physics and a Fellow in Clare Hall at the University of Cambridge in England, he succeeded Stephen Hawking on 1 November 2009...
and John H. Schwarz that anomalies in type I string theory cancel sparked the 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 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" in the early Nineties. It opened the way to the construction of entire new classes of string spectra with or without supersymmetry. Joseph Polchinski
Joseph Polchinski
Joseph Polchinski is a physicist working on string theory. He graduated from Canyon del Oro High School in Tucson, Arizona in 1971, obtained his B.S. degree from Caltech in 1975, and his Ph.D. from the University of California, Berkeley in 1980 under the supervision of Stanley Mandelstam...
's work on D-branes provided a geometrical interpretation for these results in terms of extended objects (D brane, orientifold
Orientifold
In theoretical physics orientifold is a generalization of the notion of orbifold, proposed by Augusto Sagnotti in 1987. The novelty is that in the case of string theory the non-trivial element of the orbifold group includes the reversal of the orientation of the string...
).
In the 1990s it was first argued by Edward Witten
Edward Witten
Edward Witten is an American theoretical physicist with a focus on mathematical physics who is currently a professor of Mathematical Physics at the Institute for Advanced Study....
that type I string theory with the string coupling constant
is equivalent to the SO(32) heterotic stringHeterotic string
In physics, a heterotic string is a peculiar mixture of the bosonic string and the superstring...
with the coupling
. This equivalence is known as S-dualityS-duality
In theoretical physics, S-duality is an equivalence of two quantum field theories or string theories. An S-duality transformation maps states and vacua with coupling constant g in one theory to states and vacua with coupling constant 1/g in the dual theory...
.
References
[1] F. Gliozzi, J. Scherk and D.I. Olive, ``Supersymmetry, Supergravity Theories And The Dual Spinor Model, Nucl. Phys. B122 (1977) 253.
[2] E. Witten, ``String theory dynamics in various dimensions, Nucl. Phys. B443 (1995) 85 [arXiv:hep-th/9503124].
[3] J. Polchinski, S. Chaudhuri and C.V. Johnson, ``Notes on D-Branes, arXiv:hep-th/9602052.
[4] C. Angelantonj and A. Sagnotti, ``Open strings, Phys. Rept. 1 [Erratum-ibid. ) 339] [arXiv:hep-th/0204089].