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 II string theory is a unified term that includes both type IIA strings and type IIB strings theories. Type II string theory accounts for two of the five consistent
superstring theories in ten dimensions. Both theories have the maximal amount of
supersymmetry
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 e ...
— namely 32
supercharge
In theoretical physics, a supercharge is a generator of supersymmetry transformations. It is an example of the general notion of a charge in physics.
Supercharge, denoted by the symbol Q, is an operator which transforms bosons into fermions, and v ...
s — in ten dimensions. Both theories are based on oriented
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. On the
worldsheet
In string theory, a worldsheet is a two-dimensional manifold which describes the embedding of a string in spacetime. The term was coined by Leonard Susskind as a direct generalization of the world line concept for a point particle in special and ...
, they differ only in the choice of
GSO projection
The GSO projection (named after Ferdinando Gliozzi, Joël Scherk, and David I. Olive) F. Gliozzi, J. Scherk and D. I. Olive, "Supersymmetry, Supergravity Theories and the Dual Spinor Model", ''Nucl. Phys. B'' 122 (1977), 253. is an ingredient u ...
.
Type IIA string theory
At low energies, type IIA string theory is described by type IIA
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 ...
in ten dimensions which is a non-
chiral
Chirality is a property of asymmetry important in several branches of science. The word ''chirality'' is derived from the Greek (''kheir''), "hand", a familiar chiral object.
An object or a system is ''chiral'' if it is distinguishable from ...
theory (i.e. left–right symmetric) with (1,1) ''d''=10 supersymmetry; the fact that the
anomalies in this theory cancel is therefore trivial.
In the 1990s it was realized 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 ...
(building on previous insights by
Michael Duff,
Paul Townsend
Paul Kingsley Townsend FRS (; born 3 March 1951) is a British physicist, currently a Professor of Theoretical Physics in Cambridge University's Department of Applied Mathematics and Theoretical Physics. He is notable for his work on string the ...
, and others) that the limit of type IIA string theory in which the string coupling goes to infinity becomes a new 11-dimensional theory called
M-theory
M-theory is a theory in physics that unifies all consistent versions of superstring theory. Edward Witten first conjectured the existence of such a theory at a string theory conference at the University of Southern California in 1995. Witten's ...
.
The mathematical treatment of type IIA string theory belongs to
symplectic topology
Symplectic geometry is a branch of differential geometry and differential topology that studies symplectic manifolds; that is, differentiable manifolds equipped with a closed, nondegenerate 2-form. Symplectic geometry has its origins in the H ...
and
algebraic geometry
Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials. Modern algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical ...
, particularly
Gromov–Witten invariant
In mathematics, specifically in symplectic topology and algebraic geometry, Gromov–Witten (GW) invariants are rational numbers that, in certain situations, count pseudoholomorphic curves meeting prescribed conditions in a given symplectic man ...
s.
Type IIB string theory
At low energies, type IIB string theory is described by type IIB supergravity in ten dimensions which is a chiral theory (left–right asymmetric) with (2,0) ''d''=10 supersymmetry; the fact that the anomalies in this theory cancel is therefore nontrivial.
In the 1990s it was realized that type IIB string theory with the string coupling constant ''g'' is equivalent to the same theory 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 theoret ...
.
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 leads to
type I string theory
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 the only one which contains ...
.
The mathematical treatment of type IIB string theory belongs to algebraic geometry, specifically the
deformation theory
In mathematics, deformation theory is the study of infinitesimal conditions associated with varying a solution ''P'' of a problem to slightly different solutions ''P''ε, where ε is a small number, or a vector of small quantities. The infinitesim ...
of complex structures originally studied by
Kunihiko Kodaira
was a Japanese mathematician known for distinguished work in algebraic geometry and the theory of complex manifolds, and as the founder of the Japanese school of algebraic geometers. He was awarded a Fields Medal in 1954, being the first Japanese ...
and
Donald C. Spencer
Donald Clayton Spencer (April 25, 1912 – December 23, 2001) was an American mathematician, known for work on deformation theory of structures arising in differential geometry, and on several complex variables from the point of view of pa ...
.
In 1997
Juan Maldacena
Juan Martín Maldacena (born September 10, 1968) is an Argentine theoretical physicist and the Carl P. Feinberg Professor in the School of Natural Sciences at the Institute for Advanced Study, Princeton. He has made significant contributions to t ...
gave some arguments indicating that type IIB string theory is equivalent to
N = 4 supersymmetric Yang–Mills theory
''N'' = 4 supersymmetric Yang–Mills (SYM) theory is a mathematical and physical model created to study particles through a simple system, similar to string theory, with conformal symmetry. It is a simplified toy theory based on Yang ...
in the
't Hooft limit; it was the first suggestion concerning the
AdS/CFT correspondence
In theoretical physics, the anti-de Sitter/conformal field theory correspondence, sometimes called Maldacena duality or gauge/gravity duality, is a conjectured relationship between two kinds of physical theories. On one side are anti-de Sitter s ...
.
[J. Maldacena, "The Large N Limit of Superconformal Field Theories and Supergravity]
arXiv:hep-th/9711200
/ref>
Relationship between the type II theories
In the late 1980s, it was realized that type IIA string theory is related to type IIB string theory by T-duality
In theoretical physics, T-duality (short for target-space duality) is an equivalence of two physical theories, which may be either quantum field theories or string theories. In the simplest example of this relationship, one of the theories descr ...
.
See also
*Superstring theory
Superstring theory is an attempt to explain all of the particles and fundamental forces of nature in one theory by modeling them as vibrations of tiny supersymmetric strings.
'Superstring theory' is a shorthand for supersymmetric string theor ...
*Type I string
In theoretical physics, type I string theory is one of five consistent supersymmetric string theory, 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 ...
*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 ...
References
String theory
{{string-theory-stub