wrapped brane in nLab

Contents

Contents

Idea

A brane worldvolume ϕ:Σ⟶X\phi \colon \Sigma \longrightarrow X is said to wrap a cycle c∈H dim(Σ)(X)c \in H_{\dim(\Sigma)}(X) in spacetime XX when the pushforward ϕ *[Σ]∈H •(X)\phi_\ast [\Sigma] \in H_\bullet(X) of the fundamental class of Σ\Sigma is the class, [c][c], of the given cycle in XX. If the pushforward is a multiple of [c][c], then the brane is said to wrap cc multiple times.

Examples

Via the identification of D-brane charge in K-theory, the K-theoretic McKay correspondence formalizes how D-branes wrap the fundamental cycles in the blow-up resultion of an ADE-singularity (Gonzalez-Sprinberg & Verdier 83)

• membrane instanton

• M5-brane instanton

• fractional M2-brane

• 3d-3d correspondence

• giant graviton

• in the Witten-Sakai-Sugimoto model (see there) for non-perturbative quantum chromodynamics baryons appear as wrapped D4-branes

graphics grabbed from Sugimoto 16

• polarized brane

• brane intersection

• Dp-D(p+2)-brane bound state

• Dp-D(p+4)-brane bound state

References

• Gérard Gonzalez-Sprinberg, Jean-Louis Verdier, Construction géométrique de la correspondance de McKay, Ann. Sci. ́École Norm. Sup.16 (1983) 409–449. (numdam)

• Shigeki Sugimoto, Skyrmion and String theory, chapter 15 in Mannque Rho, Ismail Zahed (eds.) The Multifaceted Skyrmion, World Scientific 2016 (doi:10.1142/9710)