Type II string theory

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In theoretical physics, 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 extended supersymmetry which is maximal amount of supersymmetry namely 32 supercharges in ten dimensions. Both theories are based on oriented closed strings. On the worldsheet, they differ only in the choice of GSO projection. They were first discovered by Michael Green and John Henry Schwarz in 1982, [1] with the terminology of type I and type II coined to classify the three string theories known at the time. [2]

Contents

Type IIA string theory

At low energies, type IIA string theory is described by type IIA supergravity 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. [3] Consequently the low energy type IIA supergravity theory can also be derived from the unique maximal supergravity theory in 11 dimensions (low energy version of M-theory) via a dimensional reduction. [4] [5]

The content of the massless sector of the theory (which is relevant in the low energy limit) is given by representation of SO(8) where is the irreducible vector representation, and are the irreducible representations with odd and even eigenvalues of the fermionic parity operator often called co-spinor and spinor representations. [6] [7] [8] These three representations enjoy a triality symmetry which is evident from its Dynkin diagram. The four sectors of the massless spectrum after GSO projection and decomposition into irreducible representations are [4] [5] [8]

where and stands for Ramond and Neveu–Schwarz sectors respectively. The numbers denote the dimension of the irreducible representation and equivalently the number of components of the corresponding fields. The various massless fields obtained are the graviton with two superpartner gravitinos which gives rise to local spacetime supersymmetry, [5] a scalar dilaton with two superpartner spinors the dilatinos , a 2-form spin-2 gauge field often called the Kalb–Ramond field, a 1-form and a 3-form . Since the -form gauge fields naturally couple to extended objects with dimensional world-volume, Type IIA string theory naturally incorporates various extended objects like D0, D2, D4 and D6 branes (using Hodge duality) among the D-branes (which are charged) and F1 string and NS5 brane among other objects. [5] [9] [8]

The mathematical treatment of type IIA string theory belongs to symplectic topology and algebraic geometry, particularly Gromov–Witten invariants.

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.

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.

In 1997 Juan Maldacena gave some arguments indicating that type IIB string theory is equivalent to N = 4 supersymmetric Yang–Mills theory in the 't Hooft limit; it was the first suggestion concerning the AdS/CFT correspondence. [10]

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.

See also

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In supersymmetry, eleven-dimensional supergravity is the theory of supergravity in the highest number of dimensions allowed for a supersymmetric theory. It contains a graviton, a gravitino, and a 3-form gauge field, with their interactions uniquely fixed by supersymmetry. Discovered in 1978 by Eugène Cremmer, Bernard Julia, and Joël Scherk, it quickly became a popular candidate for a theory of everything during the 1980s. However, interest in it soon faded due to numerous difficulties that arise when trying to construct physically realistic models. It came back to prominence in the mid-1990s when it was found to be the low energy limit of M-theory, making it crucial for understanding various aspects of string theory.

In supersymmetry, type IIA supergravity is the unique supergravity in ten dimensions with two supercharges of opposite chirality. It was first constructed in 1984 by a dimensional reduction of eleven-dimensional supergravity on a circle. The other supergravities in ten dimensions are type IIB supergravity, which has two supercharges of the same chirality, and type I supergravity, which has a single supercharge. In 1986 a deformation of the theory was discovered which gives mass to one of the fields and is known as massive type IIA supergravity. Type IIA supergravity plays a very important role in string theory as it is the low-energy limit of type IIA string theory.

In supersymmetry, type IIB supergravity is the unique supergravity in ten dimensions with two supercharges of the same chirality. It was first constructed in 1983 by John Schwarz and independently by Paul Howe and Peter West at the level of its equations of motion. While it does not admit a fully covariant action due to the presence of a self-dual field, it can be described by an action if the self-duality condition is imposed by hand on the resulting equations of motion. The other types of supergravity in ten dimensions are type IIA supergravity, which has two supercharges of opposing chirality, and type I supergravity, which has a single supercharge. The theory plays an important role in modern physics since it is the low-energy limit of type IIB string theory.

In supersymmetry, type I supergravity is the theory of supergravity in ten dimensions with a single supercharge. It consists of a single supergravity multiplet and a single Yang–Mills multiplet. The full non-abelian action was first derived in 1983 by George Chapline and Nicholas Manton. Classically the theory can admit any gauge group, but a consistent quantum theory resulting in anomaly cancellation only exists if the gauge group is either or . Both these supergravities are realised as the low-energy limits of string theories, in particular of type I string theory and of the two heterotic string theories.

References

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