nLab
D6-brane

Contents

Idea

The D-brane of dimension 6+1 in type IIA string theory.

Relation to other branes

To the KK-monopole in M-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 0R_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 0R_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.

To D7-branes

The T-dual of the D6 branes is the D7-brane in type IIB string theory.

Table of branes

from M-branes to F-branes: superstrings, D-branes and NS5-branes

M-theory on S A 1×S B 1S^1_A \times S^1_B-elliptic fibrationKK-compactification on S A 1S^1_Atype IIA string theoryT-dual KK-compactification on S B 1S^1_Btype IIB string theoryF-theory on elliptically fibered-K3 fibrationduality between F-theory and heterotic string theoryheterotic string theory on elliptic fibration
M2-brane wrapping S A 1S_A^1double dimensional reduction \mapstotype IIA superstring\mapstotype IIB superstring\mapstoheterotic superstring
M2-brane wrapping S B 1S_B^1\mapstoD2-brane\mapstoD1-brane
M2-brane wrapping pp times around S A 1S_A^1 and qq times around S B 1S_B^1\mapstopp strings and qq D2-branes\mapsto(p,q)-string
M5-brane wrapping S A 1S_A^1double dimensional reduction \mapstoD4-brane\mapstoD5-brane
M5-brane wrapping S B 1S_B^1\mapstoNS5-brane\mapstoNS5-brane\mapstoNS5-brane
M5-brane wrapping pp times around S A 1S_A^1 and qq times around S B 1S_B^1\mapstopp D4-brane and qq NS5-branes\mapsto(p,q)5-brane
M5-brane wrapping S A 1×S B 1S_A^1 \times S_B^1\mapsto\mapstoD3-brane
KK-monopole/A-type ADE singularity (degeneration locus of S A 1S^1_A-circle fibration, Sen limit of S A 1×S B 1S^1_A \times S^1_B elliptic fibration)\mapstoD6-brane\mapstoD7-branesA-type nodal curve cycle degenertion locus of elliptic fibration ADE 2Cycle (Sen 97, section 2)SU-gauge enhancement
KK-monopole orientifold/D-type ADE singularity\mapstoD6-brane with O6-planes\mapstoD7-branes with O7-planesD-type nodal curve cycle degenertion locus of elliptic fibration ADE 2Cycle (Sen 97, section 3)SO-gauge enhancement
exceptional ADE-singularity\mapsto\mapstoexceptional ADE-singularity of elliptic fibration\mapstoE6-, E7-, E8-gauge enhancement

(e.g. Johnson 97, Blumenhagen 10)

Phenomenology – Intersecting D-brane models

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.

Table of branes appearing in supergravity/string theory (for classification see at brane scan).

branein supergravitycharged under gauge fieldhas worldvolume theory
black branesupergravityhigher gauge fieldSCFT
D-branetype IIRR-fieldsuper Yang-Mills theory
(D=2n)(D = 2n)type IIA\,\,
D0-brane\,\,BFSS matrix model
D2-brane\,\,\,
D4-brane\,\,D=5 super Yang-Mills theory with Khovanov homology observables
D6-brane\,\,D=7 super Yang-Mills theory
D8-brane\,\,
(D=2n+1)(D = 2n+1)type IIB\,\,
D(-1)-brane\,\,\,
D1-brane\,\,2d CFT with BH entropy
D3-brane\,\,N=4 D=4 super Yang-Mills theory
D5-brane\,\,\,
D7-brane\,\,\,
D9-brane\,\,\,
(p,q)-string\,\,\,
(D25-brane)(bosonic string theory)
NS-branetype I, II, heteroticcircle n-connection\,
string\,B2-field2d SCFT
NS5-brane\,B6-fieldlittle string theory
D-brane for topological string\,
A-brane\,
B-brane\,
M-brane11D SuGra/M-theorycircle n-connection\,
M2-brane\,C3-fieldABJM theory, BLG model
M5-brane\,C6-field6d (2,0)-superconformal QFT
M9-brane/O9-planeheterotic string theory
M-wave
topological M2-branetopological M-theoryC3-field on G2-manifold
topological M5-brane\,C6-field on G2-manifold
solitons on M5-brane6d (2,0)-superconformal QFT
self-dual stringself-dual B-field
3-brane in 6d

References

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

Revised on February 5, 2017 04:13:23 by Urs Schreiber (195.229.110.3)