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 experi ...

, 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 strings, but also

open strings ''Open Strings'' is an album by French jazz fusion artist Jean-Luc Ponty, released in 1971 on vinyl by the MPS label. Track listing All songs written by Jean-Luc Ponty, except where noted. Side one #"Flipping, Pt.1" – 4:40 #"Flipping, Pt.2 ...

Overview

The classic 1976 work of Ferdinando Gliozzi, Joël 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. 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 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 th ...

of type IIB string theory, with 32 half- D9-branes 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 theorie ...

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 Polchi ...

). 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, ...

that type I string theory with the string coupling constant

g

is equivalent to the SO(32)

heterotic string In string theory, a heterotic string is a closed string (or loop) which is a hybrid ('heterotic') of a superstring and a bosonic string. There are two kinds of heterotic string, the heterotic SO(32) and the heterotic E8 × E8, abbreviat ...

with the coupling

1/g

. 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 theore ...

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
String theory">Erratum-ibid.) 339
arXiv:hep-th/0204089
String theory {{String-theory-stub