|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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Action PrincipleEdit this section
Compactification of mismatched dimensionsEdit this section
With this action for the Type H String Theory being different from the ordinary RNS Action, we have the issue of imbalance between bosons and fermions out of the way. Now, we need to tackle the problem of the left-movers being in 26 dimensions and the right-movers being in 10 dimensions. To do that, we will compactify the mismatched dimensions on a lattice. Naturally, to preserve the symmetries of the Heterotic String Action above, we need to make this lattice be unimodular.
Compactification on this lattice with "dimensionless momenta" and would lead to the following condition:
But since only the left-movers are Bosonic Strings and need to be compactified ,.
I.e. the norm-squared is even. A lattice made of such vectors is an Even Lattice, and thus, the lattice also needs to be somewhat even.
The only suitable even, unimodular, 16 dimensional lattices are and . The Type HE String Theory is the former.
Note that is also the gauge group of the Type HE string theory.
Suitability as a Theory of EverythingEdit this section
The necessity for Heterotic Strings arose when it was found that Type IIB String Theory was not suitable for the Theory of Everything and neither was Type IIA. However, the gauge group is suitable for a Theory of Everything as it can easily include the Standard Model gauge group as a Subgroup.
T-Duality with Type HO String TheoryEdit this section
Until the Second Superstring Revolution, it was thought that the Type HE String Theory and Type HO String Theory were only connected due to their mismatched forms (i.e. with the 16 mismatched dimensions uncompactified.). However, this is useless, as this is neither a duality nor an equivalence, so one may not derive one String Theory from the other this way. During the Second Superstring Revolution, it was discovered that these two are actually related by T-Duality.
The root lattice of is , whereas the root lattice of is . Since:
ReferencesEdit this section
- ↑ 1.0 1.1 1.2 McMohan, David (2008). String theory demistified. McGraw-Hill. pp. 207–219. ISBN 978-0-07-149870-8. http://www.nucleares.unam.mx/~alberto/apuntes/mcmahon.pdf.
- ↑ 2.0 2.1 2.2 Polchinski, Joseph (1998). String Theory: Volume 2. Cambridge University Press. p. 45. ISBN 978-0-521-63304-8.
- ↑ 3.0 3.1 Mohaupt, Thomas (2002). "Introduction to String theory". Lecture Notes in Physics. 2002 631: 173–251. arXiv:hep-th/0207249. Bibcode 2003LNP...631..173M. doi:10.1007/978-3-540-45230-0_5. ISBN 978-3-540-40810-9.