Contents

Type II string theory

This article needs additional citations for verification. Please help improve this articlebyadding citations to reliable sources. Unsourced material may be challenged and removed. Find sources: "Type II string theory" – news · newspapers · books · scholar · JSTOR (April 2014) (Learn how and when to remove this message)

String theory
Fundamental objects
String Cosmic string Brane D-brane
Perturbative theory
Bosonic Superstring (Type I, Type II, Heterotic)
Non-perturbative results
S-duality T-duality U-duality M-theory F-theory AdS/CFT correspondence
Phenomenology
Phenomenology Cosmology Landscape
Mathematics
Geometric Langlands correspondence Mirror symmetry Monstrous moonshine Vertex algebra K-theory
Related concepts Theory of everything Conformal field theory Quantum gravity Supersymmetry Supergravity Twistor string theory N = 4 supersymmetric Yang–Mills theory Kaluza–Klein theory Multiverse Holographic principle
Theorists Aganagić Arkani-Hamed Atiyah Banks Berenstein Bousso Curtright Dijkgraaf Distler Douglas Duff Dvali Ferrara Fischler Friedan Gates Gliozzi Gopakumar Green Greene Gross Gubser Gukov Guth Hanson Harvey Hořava Horowitz Gibbons Kachru Kaku Kallosh Kaluza Kapustin Klebanov Knizhnik Kontsevich Klein Linde Maldacena Mandelstam Marolf Martinec Minwalla Moore Motl Mukhi Myers Nanopoulos Năstase Nekrasov Neveu Nielsen van Nieuwenhuizen Novikov Olive Ooguri Ovrut Polchinski Polyakov Rajaraman Ramond Randall Randjbar-Daemi Roček Rohm Sagnotti Scherk Schwarz Seiberg Sen Shenker Siegel Silverstein Sơn Staudacher Steinhardt Strominger Sundrum Susskind 't Hooft Townsend Trivedi Turok Vafa Veneziano Verlinde Verlinde Wess Witten Yau Yoneya Zamolodchikov Zamolodchikov Zaslow Zumino Zwiebach
History Glossary
v t e

Intheoretical 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 ${\displaystyle {\mathcal {N}}=2}$ 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.

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.^[1] 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.^[2][3]

The content of the massless sector of the theory (which is relevant in the low energy limit) is given by ${\textstyle (8_{v}\oplus 8_{s})\otimes (8_{v}\oplus 8_{c})}$ representation of SO(8) where ${\displaystyle 8_{v}}$ is the irreducible vector representation, ${\displaystyle 8_{c}}$ and ${\displaystyle 8_{s}}$ are the irreducible representations with odd and even eigenvalues of the fermionic parity operator often called co-spinor and spinor representations.^[4][5][6] 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 ^[2][3][6]

${\displaystyle {\text{NS-NS}}:~8_{v}\otimes 8_{v}=1\oplus 28\oplus 35=\Phi \oplus B_{\mu \nu }\oplus G_{\mu \nu }}$

${\displaystyle {\text{NS-R}}:8_{v}\otimes 8_{c}=8_{s}\oplus 56_{c}=\lambda ^{+}\oplus \psi _{m}^{-}}$

${\displaystyle {\text{R-NS}}:8_{c}\otimes 8_{s}=8_{s}\oplus 56_{s}=\lambda ^{-}\oplus \psi _{m}^{+}}$

${\displaystyle {\text{R-R}}:8_{s}\otimes 8_{c}=8_{v}\oplus 56_{t}=C_{n}\oplus C_{nmp}}$

where ${\displaystyle {\text{R}}}$ and ${\displaystyle {\text{NS}}}$ 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 ${\displaystyle G_{\mu \nu }}$ with two superpartner gravitinos ${\displaystyle \psi _{m}^{\pm }}$ which gives rise to local spacetime supersymmetry,^[3] a scalar dilaton ${\displaystyle \Phi }$ with two superpartner spinors—the dilatinos ${\displaystyle \lambda ^{\pm }}$, a 2-form spin-2 gauge field ${\displaystyle B_{\mu \nu }}$ often called the Kalb-Ramond field, a 1-form ${\displaystyle C_{n}}$ and a 3-form ${\displaystyle C_{nmp}}$. Since the ${\displaystyle {\text{p}}}$-form gauge fields naturally couple to extended objects with ${\displaystyle {\text{p+1}}}$ dimensional world-volume, Type II-A string theory naturally incorporates various extended objects like D0, D2, D4 and D6 branes (using Hodge duality) among the D-branes (which are ${\displaystyle {\text{R}}}$${\displaystyle {\text{R}}}$ charged) and F1 string and NS5 brane among other objects.^[3][7][6]

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

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.^[8]

In the late 1980s, it was realized that type IIA string theory is related to type IIB string theory by T-duality.

• Superstring theory
• Type I string
• Heterotic string

This string theory-related article is a stub. You can help Wikipedia by expanding it.