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 N = 2 {\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. They were first discovered by Michael Green and John Henry Schwarz in 1982, with the terminology of type I and type II coined to classify the three string theories known at the time.
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. 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. The content of the massless sector of the theory (which is relevant in the low energy limit) is given by ( 8 v ⊕ 8 s ) ⊗ ( 8 v ⊕ 8 c ) {\textstyle (8_{v}\oplus 8_{s})\otimes (8_{v}\oplus 8_{c})} representation of SO(8) where 8 v {\displaystyle 8_{v}} is the irreducible vector representation, 8 c {\displaystyle 8_{c}} and 8 s {\displaystyle 8_{s}} are the irreducible representations with odd and even eigenvalues of the fermionic parity operator often called co-spinor and spinor representations. 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
NS-NS : 8 v ⊗ 8 v = 1 ⊕ 28 ⊕ 35 = Φ ⊕ B μ ν ⊕ G μ ν {\displaystyle {\text{NS-NS}}:~8_{v}\otimes 8_{v}=1\oplus 28\oplus 35=\Phi \oplus B_{\mu \nu }\oplus G_{\mu \nu }}
NS-R : 8 v ⊗ 8 c = 8 s ⊕ 56 c = λ + ⊕ ψ m − {\displaystyle {\text{NS-R}}:8_{v}\otimes 8_{c}=8_{s}\oplus 56_{c}=\lambda ^{+}\oplus \psi _{m}^{-}}
R-NS : 8 c ⊗ 8 s = 8 s ⊕ 56 s = λ − ⊕ ψ m + {\displaystyle {\text{R-NS}}:8_{c}\otimes 8_{s}=8_{s}\oplus 56_{s}=\lambda ^{-}\oplus \psi _{m}^{+}}
R-R : 8 s ⊗ 8 c = 8 v ⊕ 56 t = C n ⊕ C n m p {\displaystyle {\text{R-R}}:8_{s}\otimes 8_{c}=8_{v}\oplus 56_{t}=C_{n}\oplus C_{nmp}}
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