In
theoretical physics
Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain and predict natural phenomena. This is in contrast to experimental physics, which uses experim ...
, 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 the only one which contains not only
closed string
In physics, a string is a physical entity postulated in string theory and related subjects. Unlike elementary particles, which are zero-dimensional or point-like by definition, strings are one-dimensional extended entities. Researchers often h ...
s, but also
open strings.
Overview
The classic 1976 work of
Ferdinando Gliozzi,
Joël Scherk
Joël Scherk (; 27 May 1946 – 16 May 1980) was a French theoretical physicist who studied string theory and supergravity.
Work
Scherk studied in Paris at the École Normale Supérieure (ENS). In 1969 he received his diploma (Thèse de troisièm ...
and
David Olive paved the way to a systematic understanding of the rules behind string spectra in cases where only
closed string
In physics, a string is a physical entity postulated in string theory and related subjects. Unlike elementary particles, which are zero-dimensional or point-like by definition, strings are one-dimensional extended entities. Researchers often h ...
s are present via
modular invariance
In theoretical physics, modular invariance is the invariance under the group such as SL(2,Z) of large diffeomorphisms of the torus. The name comes from the classical name modular group of this group, as in modular form theory.
In string theory ...
. 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
Augusto Sagnotti (born 1955) is an Italian theoretical physicist at Scuola Normale (since 2005).
Biography
Sagnotti earned a Laurea in Electrical Engineering from the University of Rome "La Sapienza" in 1978 (advisors: Bruno Crosignani and Paol ...
in 1988,
[
] the type I string theory can be obtained as an
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(s) of the orbifold group includes the reversal of the or ...
of
type IIB string theory, with 32 half-
D9-brane
In string theory, D-branes, short for ''Dirichlet membrane'', are a class of extended objects upon which open strings can end with Dirichlet boundary conditions, after which they are named. D-branes were discovered by Jin Dai, Leigh, and Polc ...
s added in the vacuum to cancel various
anomalies giving it a gauge group of SO(32) via
Chan-Paton factors.
At low energies, type I string theory is described by the N=1
supergravity
In theoretical physics, supergravity (supergravity theory; SUGRA for short) is a modern field theory that combines the principles of supersymmetry and general relativity; this is in contrast to non-gravitational supersymmetric theories such as ...
(type I supergravity) in ten dimensions coupled to the SO(32)
supersymmetric
In a supersymmetric theory the equations for force and the equations for matter are identical. In theoretical and mathematical physics, any theory with this property has the principle of supersymmetry (SUSY). Dozens of supersymmetric theories ...
Yang–Mills theory
In mathematical physics, Yang–Mills theory is a gauge theory based on a special unitary group SU(''N''), or more generally any compact, reductive Lie algebra. Yang–Mills theory seeks to describe the behavior of elementary particles using ...
. The discovery in 1984 by
Michael Green and
John H. Schwarz that anomalies in type I string theory cancel sparked the
first superstring revolution
The history of string theory spans several decades of intense research including two superstring revolutions. Through the combined efforts of many researchers, string theory has developed into a broad and varied subject with connections to quantu ...
. 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
Tor Vergata University of Rome, also known as the University of Rome II ( it, Università degli Studi di Roma "Tor Vergata"), is a public research university located in Rome, Italy. Located in the southeastern suburb of Rome, the university combine ...
in the early 1990s. It opened the way to the construction of entire new classes of string spectra with or without supersymmetry.
Joseph Polchinski
Joseph Gerard Polchinski Jr. (; May 16, 1954 – February 2, 2018) was an American theoretical physicist and string theorist.
Biography
Polchinski was born in White Plains, New York, the elder of two children to Joseph Gerard Polchinski Sr. (1929 ...
's work on D-branes provided a geometrical interpretation for these results in terms of extended objects (
D-brane
In string theory, D-branes, short for ''Dirichlet membrane'', are a class of extended objects upon which open strings can end with Dirichlet boundary conditions, after which they are named. D-branes were discovered by Jin Dai, Leigh, and Polch ...
,
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(s) of the orbifold group includes the reversal of the or ...
).
In the 1990s it was first argued by
Edward Witten
Edward Witten (born August 26, 1951) is an American mathematical and theoretical physicist. He is a Professor Emeritus in the School of Natural Sciences at the Institute for Advanced Study in Princeton. Witten is a researcher in string theory, q ...
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
In theoretical physics, S-duality (short for strong–weak duality, or Sen duality) is an equivalence of two physical theories, which may be either quantum field theories or string theories. S-duality is useful for doing calculations in theoret ...
.
Notes
References
* E. Witten, "String theory dynamics in various dimensions", ''Nucl. Phys. B'' 443 (1995) 85
arXiv:hep-th/9503124
* J. Polchinski, S. Chaudhuri and C.V. Johnson, "Notes on D-Branes"
arXiv:hep-th/9602052
* C. Angelantonj and A. Sagnotti, "Open strings", ''Phys. Rep.'' 1
arXiv:hep-th/0204089
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String theory
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