type II string theory
Critical string models
Perturbative string theory is defined in terms of certain classes of 2d CFTs. Depending on which class that is, one speaks of different types of string theory.
The effective quantum field theory of type II string theory containts –besides type II supergravity – the self-dual higher gauge theory of RR-fields and Kalb-Ramond fields.
Apart from the Weyl anomaly?, which cancels for 10-dimensional target spaces, the action functional of the string-sigma-model also in general has an anomalous action functional , for two reasons:
The higher holonomy of the higher background gauge fields is in general not a function, but a section of a line bundle;
The fermionic path integral over the worldsheet-spinors of the superstring produces as section of a Pfaffian line bundle.
In order for the action functional to be well-defined, the tensor product of these different anomaly line bundles over the bosonic configuration space must have trivial class (as bundles with connection, even). This gives rise to various further anomaly cancellation conditions:
For the open type II string the condition is known as the Freed-Witten anomaly cancellation condition: it says that the restriction of the B-field to any D-brane must consistute the twist of a twisted spin^c structure on the brane.
A more detailed analysis of these type II anomalies is in (DFMI) and (DFMII).
By a holographic principle realized in this case as AdS/CFT correspondence (see the references there), type II string theory is supposed to be dual to 4-dimensional super Yang-Mills theory.
A canonical textbook source is
Eric D'Hoker, String theory – lecture 7: Free superstrings , in part 3 of
Pierre Deligne, Pavel Etingof, Dan Freed, L. Jeffrey, David Kazhdan, John Morgan, D.R. Morrison and Edward Witten, eds. Quantum Fields and Strings, A course for mathematicians, 2 vols. Amer. Math. Soc. Providence 1999. (web version)
Discussion of type II quantum anomalies is in
An exposition is at
- Dan Freed, Lectures on K-theory and orientifolds (2012) (pdf)
Classical solutions / vacua
Description of type II backgrounds in terms of generalized complex geometry/Courant Lie 2-algebroids is in
- Mariana Grana, Francesco Orsi, N=1 vacua in Exceptional Generalized Geometry (arXiv:1105.4855)
A holographic description of type II by higher dimensional Chern-Simons theory is discussed in
Revised on May 21, 2013 19:26:39
by Urs Schreiber