# Type II String Theory

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String Theory
Prior to the First Superstring Revolution
Early History S-Matrix Theory
Regge Trajectory
Bosonic String Theory Worldsheet
String
Bosonic String Theory
String Perturbation Theory
Tachyon Condensation
Supersymmetric Revolution Supersymmetry
RNS Formalism
GS Formalism
BPS
Superstring Revolutions
First Superstring Revolution GSO Projection
Type II String Theory
Type IIB String Theory
Type IIA String Theory
Type I String Theory
Type H String Theory
Type HO String Theory
Type HE String Theory
Second Superstring Revolution T-Duality
D-Brane
S-Duality
Horava-Witten String Theory
M-Theory
Holographic Principle
N=4 Super-Yang-Mills Theory
BFSS Matrix Theory
Matrix String Theory
(2,0) Theory
Twistor String Theory
F-Theory
String Field Theory
Pure Spinor Formalism
After the Revolutions
Phenomenology String Theory Landscape
Minimal Supersymmetric Standard Model
String Phenomenology

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In String Theory, Type II String Theory is a unified term that includes both Type IIA String Theory and Type IIB String Theory. These account for two of the five consistent Superstring Theories in ten dimensions. Both theories have the 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.

## Type IIB String TheoryEdit this section

Main Article: Type IIB String Theory

Orientifold of Type IIB String Theory, when combined with the Open String sector, leads to Type I String Theory.

The Type IIB String Theory action is simply the Ramond-Neveu-Schwarz Action.[1] The Lagrangian Density (whose double integral across the Worldsheet is the action) is:

${{\mathsf{\mathcal{L}}}_{RNS}}=\frac{T}{2} h^{\alpha \beta} \left( \partial_\alpha X^\mu \partial_\beta X^\nu +i\hbar c_0 \bar{\psi_\mu} \not\partial \psi^\mu \right) g_{\mu\nu}$

The GSO Projection in the Ramond Ramond sector is such that the left-moving and right-moving sectors have the same GSO Projections.

## Type IIA String TheoryEdit this section

Main Article: Type IIA String Theory

The Type IIA String Theory action is simply the Ramond-Neveu-Schwarz Action.[1] The Lagrangian Density (whose double integral across the Worldsheet is the action) is:

$\mathcal{L_{RNS}} = {\frac{T }{2c_0}}h^{ab} \left(\partial_a X^\mu \partial_b X^\nu-2\psi_+^\mu\left(\frac{\partial \psi_-^\mu}{\partial \sigma}-\frac{\partial\psi_-^\mu}{\partial \tau}\right)\right)g_{\mu \nu}$

The GSO Projection in the Ramond Ramond sector is such that the left-moving and right-moving sectors have opposite GSO Projections,.

## T-duality and Type II string theoryEdit this section

Prior to the Second Superstring Revolution, the only known relationship between the Type IIB String Theory and the Type IIA String Theory was that both of them were GSO Truncated versions of the naive RNS String Theory, by applying the same and opposite GSO Projections to the left- and right- moving components of the state respectively. However, this relationship, was not a duality or an equivalence, and thus, it could not be used to derive one theory from the other.

During the start of the Second Superstring Revolution, it was realized that Type IIA String Theory is related to Type IIB String Theory by T-Duality.[1]

The reason is that it is clear that T-duality negates the sign of the massless bosonic directional dimensional field $X^\mu$, much as how S-duality negates the sign of the Dilaton field $\Phi$. Thus, by Worldsheet Supersymmetry, it should also negate the massless fermionic directional dimensional field $\mathbf{\psi}^\mu$ and therefore the Fermionic operator - valued modes of oscillation of the string $\hat d_{\mu}$ are Wick-Rotated. So, therefore, the fermion number operator $F$ is also negated, and therefore, thus, the Klein Operator is also negated, and hence, thus, the GSO Projection $\mathcal P_{\operatorname{GSO}}$ transforms from the same on the left-moving component $|\psi_-\rangle$ and the right-moving component $|\psi_+\rangle$ to the opposite on the left- and right- components. This clearly transforms between the Type IIA String Theory and the Type IIB String Theory, unifying them into a single Type II String Theory.

## GS FormalismEdit this section

In the GS Formalism, Type II String Theory has $\mathcal N=2$ Supersymmetry, which means that the spinor $\Theta^A$ has two components.