nLab
D7-brane

Idea

The D-brane in type IIB string theory of dimension $7+1$.

In F-theory these are the degenration loci of the axio-dilaton elliptic fibration, where the discriminant $\Delta$ of the elliptic curve fibers vanishes and the fiber degenrates to the nodal curve (e.g. Sen 97, Blumenhagen 10, (11)).

Relation to other branes

The D7-branes arise from the D6-branes in type IIA string theory under T-duality.

from to F-branes: , and

on $S^1_A \times S^1_B$-	on $S^1_A$		on $S^1_B$		on - fibration		on
$S_A^1$	$\mapsto$		$\mapsto$			$\mapsto$
$S_B^1$	$\mapsto$		$\mapsto$
$p$ times around $S_A^1$ and $q$ times around $S_B^1$	$\mapsto$	$p$ and $q$	$\mapsto$
$S_A^1$	$\mapsto$		$\mapsto$
$S_B^1$	$\mapsto$		$\mapsto$			$\mapsto$
$p$ times around $S_A^1$ and $q$ times around $S_B^1$	$\mapsto$	$p$ and $q$	$\mapsto$
$S_A^1 \times S_B^1$	$\mapsto$		$\mapsto$
/ (degeneration locus of $S^1_A$-circle fibration, of $S^1_A \times S^1_B$ )	$\mapsto$		$\mapsto$		A-type cycle degenertion locus of (Sen 97, section 2)		-
/	$\mapsto$	with	$\mapsto$	with	D-type cycle degenertion locus of (Sen 97, section 3)		-
exceptional	$\mapsto$		$\mapsto$		exceptional ADE-singularity of elliptic fibration	$\mapsto$	-, -, -

(e.g. Johnson 97, Blumenhagen 10)

Related concepts

Table of appearing in / (for classification see at ).

	in	d under	has theory
$(D = 2n)$		$\,$	$\,$
	$\,$	$\,$
	$\,$	$\,$	$\,$
	$\,$	$\,$	with
	$\,$	$\,$
	$\,$	$\,$
$(D = 2n+1)$		$\,$	$\,$
	$\,$	$\,$	$\,$
	$\,$	$\,$	2d with
	$\,$	$\,$
	$\,$	$\,$	$\,$
	$\,$	$\,$	$\,$
	$\,$	$\,$	$\,$
	$\,$	$\,$	$\,$
()	()
			$\,$
	$\,$
	$\,$
D-brane for			$\,$
			$\,$
			$\,$
	/		$\,$
	$\,$		,
	$\,$
/
		on
	$\,$	on
on

See also F-theory.

References

As a black brane the D7 is identified in

• Eric Bergshoeff, Mees de Roo, Michael Green, G. Papadopoulos, Paul Townsend, Duality of Type II 7-branes and 8-branes, Nucl. Phys.B470:113-135, 1996 (arXiv:hep-th/9601150)

The Green-Schwarz sigma-model description of $(p,q)$-7-branes via cocycles on extended super Minkowski spacetimes is obtained in

• Makoto Sakaguchi, section 2 of IIB-Branes and New Spacetime Superalgebras, JHEP 0004 (2000) 019 (arXiv:hep-th/9909143)

See also

• Oliver DeWolfe, Tamas Hauer, Amer Iqbal, Barton Zwiebach, Uncovering Infinite Symmetries on [p,q] 7-branes: Kac-Moody Algebras and Beyond (arXiv:hep-th/9812209)

• Ashoke Sen, Orientifold Limit of F-theory Vacua (arXiv:hep-th/9702165)

• Blumenhagen, Basics of F-theory from the Type IIB Perspective (arXiv:1002.2836)

In

• P. Meessen, T. Ortin, An $Sl(2,\mathbb{Z})$ Multiplet of Nine-Dimensional Type II Supergravity Theories (arXiv:hep-th/9806120)

it is argued that 7-branes in type II string theory form not just a doublet, but a triplet under S-duality.