Type II string theory
Encyclopedia
In theoretical physics
, type II string theory is a unified term that includes both type IIA strings and type IIB strings. These account for two of the five consistent superstring theories
in ten dimensions. Both theories have the maximal amount of supersymmetry
— namely 32 supercharge
s — in ten dimensions. Both theories are based on oriented closed strings. On the worldsheet
, they differ only in the choice of GSO projection
.
in ten dimensions which is a non-chiral
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
(building on previous insights by Michael Duff, Paul Townsend, 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
.
The mathematical treatment of type IIA string theory belongs to symplectic topology
and algebraic geometry
, particularly Gromov-Witten invariant
s.
In the 1990s it was realized that type II string theory with the string coupling constant
is equivalent to the same theory with the coupling 
. This equivalence is known as S-duality
.
Orientifold
of type IIB string theory leads to type I string theory
.
The mathematical treatment of type IIB string theory belongs to algebraic geometry, specifically the deformation theory
of complex structures originally studied by Kunihiko Kodaira and Donald C. Spencer
.
.
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 II string theory is a unified term that includes both type IIA strings and type IIB strings. These account for two of the five consistent superstring theories
Superstring theory
Superstring theory is an attempt to explain all of the particles and fundamental forces of nature in one theory by modelling them as vibrations of tiny supersymmetric strings...
in ten dimensions. Both theories have the maximal amount of supersymmetry
Supersymmetry
In particle physics, supersymmetry is a symmetry that relates elementary particles of one spin to other particles that differ by half a unit of spin and are known as superpartners...
— namely 32 supercharge
Supercharge
In theoretical physics, a supercharge is a generator of supersymmetry transformations.Supercharge, denoted by the symbol Q, is an operator which transforms bosons into fermions, and vice versa...
s — in ten dimensions. Both theories are based on oriented closed strings. On the worldsheet
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 around 1967 as a direct generalization of the world line concept for a point particle in special and general relativity.The type of string,...
, they differ only in the choice of GSO projection
GSO projection
The GSO projection is an ingredient used in constructing a consistent model in superstring theory. The projection is a selection of a subset of possible vertex operators in the worldsheet conformal field theory --usually those with specific worldsheet fermion number and periodicity conditions...
.
Type IIA string
At low energies, type IIA string theory is described by type IIA supergravitySupergravity
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...
in ten dimensions which is a non-chiral
Chirality (physics)
A chiral phenomenon is one that is not identical to its mirror image . The spin of a particle may be used to define a handedness for that particle. A symmetry transformation between the two is called parity...
theory (i.e. left-right symmetric) with (1,1) d=10 supersymmetry; the fact that the 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...
in this theory cancel is therefore trivial.
In the 1990s it was realized 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....
(building on previous insights by Michael Duff, Paul Townsend, 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
In theoretical physics, M-theory is an extension of string theory in which 11 dimensions are identified. Because the dimensionality exceeds that of superstring theories in 10 dimensions, proponents believe that the 11-dimensional theory unites all five string theories...
.
The mathematical treatment of type IIA string theory belongs to symplectic topology
Symplectic topology
Symplectic geometry is a branch of differential geometry and differential topology which studies symplectic manifolds; that is, differentiable manifolds equipped with a closed, nondegenerate 2-form...
and algebraic geometry
Algebraic geometry
Algebraic geometry is a branch of mathematics which combines techniques of abstract algebra, especially commutative algebra, with the language and the problems of geometry. It occupies a central place in modern mathematics and has multiple conceptual connections with such diverse fields as complex...
, particularly Gromov-Witten invariant
Gromov-Witten invariant
In mathematics, specifically in symplectic topology and algebraic geometry, Gromov–Witten invariants are rational numbers that, in certain situations, count pseudoholomorphic curves meeting prescribed conditions in a given symplectic manifold...
s.
Type IIB string
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 II string theory with the string coupling constant
is equivalent to the same theory 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...
.
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 leads to type I string theory
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 and which contains not only closed strings, but also open strings.The classic 1976 work of Ferdinando Gliozzi, Joel Scherk and...
.
The mathematical treatment of type IIB string theory belongs to algebraic geometry, specifically the deformation theory
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 Pε, where ε is a small number, or vector of small quantities. The infinitesimal conditions are therefore the result of applying the approach...
of complex structures originally studied by Kunihiko Kodaira and Donald C. Spencer
Donald C. Spencer
Donald Clayton Spencer was an American mathematician, known for major work on deformation theory of structures arising in differential geometry, and on several complex variables from the point of view of partial differential equations. He was born in Boulder, Colorado, and educated at the...
.
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-dualityT-duality
T-duality is a symmetry of quantum field theories with differing classical descriptions, of which the relationship between small and large distances in various string theories is a special case. Discussion of the subject originated in a paper by T. S. Buscher and was further developed by Martin...
.
See also
- superstring theorySuperstring theorySuperstring theory is an attempt to explain all of the particles and fundamental forces of nature in one theory by modelling them as vibrations of tiny supersymmetric strings...
- type I string
- heterotic stringHeterotic stringIn physics, a heterotic string is a peculiar mixture of the bosonic string and the superstring...