|All Roads Lead to String Theory (Polchinski)|
Prior to the First Superstring Revolution
|Early History|| S-Matrix Theory|
|Bosonic String Theory|| Worldsheet|
Bosonic String Theory
String Perturbation Theory
|Supersymmetric Revolution|| Supersymmetry|
|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|
Horava-Witten String Theory
N=4 Super-Yang-Mills Theory
BFSS Matrix Theory
Matrix String Theory
Twistor String Theory
String Field Theory
Pure Spinor Formalism
After the Revolutions
|Phenomenology|| String Theory Landscape|
Minimal Supersymmetric Standard Model
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Type IIB String Theory is a consistent 10-dimensional Superstring Theory. It has a Supersymmetry of (32 supercharges), or more specifically, , in string - theoretical terms, as opposed to Supergravity terms. It is GSO Truncated, so it does not have a Tachyon in its ground state. It is distinguished from the Type IIA String Theory by its same Ramond Sector GSO Projection on both left- and right- moving components of the state. This makes the theory non-chiral.
Action PrincipleEdit this section
Consequently, the action is:
GSO ProjectionEdit this section
Or the following pair:
Cancellation of Conformal AnomalyEdit this section
Since the Type IIB String Theory is only a GSO Truncated version of the naive RNS String Theory, its normal ordering constant is in the Ramond Sector and and its critical dimension is in order for cancellation of conformal anomaly to occur.
Gauge Group and Unsuitabilitiy as a Theory of EverythingEdit this section
The Type IIB String Theory is non-chiral, and consequently has no gauge group (unless the identity group is counted). This is fine as a theory of quantum gravity, because a gauge group isn't required to describe gravity (in fact, it can be checked, that since it is a GSO Truncated version of naive RNS String Theory, getting rid of Supersymmetry from the naive RNS String Theory results in the Bosonic String Theory, and when its beta function is set to 0 to preserve Conformal invariance, one obtains the Einstein Field Equations, and thus General Relativity at the low-energy-limit). However, this would describe the other interactions, such as the strong force, the weak force and the Electromagnetic force incorrectly, as the experimentally verified Standard Model requires them to have gauge groups of , and respectively.
Therefore, the Type IIB String Theory, even when compactified on a Calabi-Yau Manifold, cannot be a Theory of Everything. This initiated the main part of the First Superstring Revolution and the Type H String Theoryies. The Type HE string theory satisfies this requirement.
T-duality with the Type IIA 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.
The reason is that it is clear that T-Duality negates the sign of the massless bosonic directional dimensional field , much as how S-duality negates the sign of the Dilaton field . Thus, by Worldsheet Supersymmetry, it should also negate the massless fermionic directional dimensional field and therefore the Fermionic operator - valued modes of oscillation of the string are Wick-rotated. So, therefore, the fermion number operator is also negated, and therefore, thus, the Klein Operator is also negated, and hence, thus, the GSO Projection transforms from the same on the left-moving component and the right-moving component 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.
S-duality with the "Sen string theory"Edit this section
It is generally very difficult to find the strong-coupling limit of any theory, if it is in the peturbative regime, because this strong-coupling limit would obviously diverge. However, if one anaanalyses the massless fields of Type IIB String Theory, one sees that the fields , at strong coupling become unchanged, except with the F1 Strings transforming into the D1 Branes. Thus, the S-dual of the Type IIB String Theory is the Type IIB String Theory with the F1 Strings replaced with the D1 branes, which is occasionally called the Sen String Theory.
GS FormalismEdit this section
Furthermore, it is uniquely identified by the projection:
Which makes it non-chiral.
ReferencesEdit this section
- ↑ 1.0 1.1 1.2 1.3 Mohaupt, Thomas. Introduction to String theory. http://arxiv.org/pdf/hep-th/0207249v1.pdf.
- ↑ 2.0 2.1 2.2 2.3 Szabo, Richard, J.. Introduction to String theory and D-brane Dynamics. http://arxiv.org/pdf/hep-th/0207142v1.pdf.
- ↑ Wray, Kevin. An Introduction to String Theory. http://math.berkeley.edu/~kwray/papers/string_theory.pdf.
- ↑ McMohan, David (2009). String theory DeMystified. Chicago: McGrawHill. ISBN 978-0071498708. http://www.nucleares.unam.mx/~alberto/apuntes/mcmahon.pdf.
- ↑ Feynman, Richard; Albert (2005). Styer. ed. Quantum Mechanics and Path Integrals (2 ed.). New York: Dover. p. 356. ISBN 978-0486477220.