The D-brane of dimension 6+1 in type IIA string theory.
The lift of the D6 to M-theory is the Kaluza-Klein monopole there (Townsend 95).
One way to understand this is as follows: the first Chern class of the M-theory circle bundle is the D0-brane degree-2 RR-field strength $R_0$. By the self-duality of the RR-fields this is the Hodge dual of the D6-brane degree-8 field strength. Now given a Kaluza-Klein monopole after removing the locus of the monopole where the circle-fiber degenerates (as in the original Dirac charge quantization argument) it is a non-degenerated circle bundle such that the integral of the 2-form $R_0$ over any 2-sphere surrounding the singular locus is non-trivial. By the usual yoga of electric-magnetic duality this integral measures the magnetic flux of a D6-brane sitting at the singular locus. For more on this see at Kaluza-Klein monopole – Relation to the D6-brane, and see at M-theory lift of gauge enhancement on D6-branes.
The T-dual of the D6 branes is the D7-brane in type IIB string theory.
from M-branes to F-branes: superstrings, D-branes and NS5-branes
(e.g. Johnson 97, Blumenhagen 10)
D6-branes are the main ingredient in type IIA string phenomenology in the guise of intersecting D-brane models, see also at string phenomenology the section Models in type II with intersecting branes.
graphics grabbed from Ibáñez-Uranga 12
Table of branes appearing in supergravity/string theory (for classification see at brane scan).
The relation to the Kaluza-Klein monopole in M-theory is due to
Further discussion and derivation of the Chan-Paton gauge field content on the D6 from the KK-monopole is discussed in
César Gómez, Juan José Manjarín, A note on the dyonic D6-brane, 6th International Workshop on Conformal Field Theory and Integrable Models, Landau Institute, Sept. 2002 (arXiv:hep-th/0302096)
Juan José Manjarín, Topics on D-brane charges with B-fields, Int. J. Geom. Meth. Mod. Phys. 1 (2004) (arXiv:hep-th/0405074)
Discussion of D6 intersecting branes for intersecting D-brane models:
Luis Ibáñez, Angel Uranga, String Theory and Particle Physics – An Introduction to String Phenomenology, Cambridge 2012
Angel Uranga, Model building in IIA: Intersecting brane worlds, 2012 (pdf)
Last revised on February 16, 2019 at 13:36:38. See the history of this page for a list of all contributions to it.