In physics (string theory), a (factor space of a) brane worldvolume is said to wrap a cycle in spacetime when the pushforward of the fundamental class of the manifold (or orbifold) is the class, , of the given cycle in . If the pushforward is a multiple of , then the brane is said to wrap multiple times.
Here is typically taken to be ordinary homology but may also be K-homology (cf. D-brane charge quantization in K-theory) and could in principle by any other generalized homology-theory thought to encode the flux quantization.
In mathematics (algebraic topology), a cycle represented by a manifold this way is said to be Steenrod representable.
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)
in the Witten-Sakai-Sugimoto model (see there) for non-perturbative quantum chromodynamics baryons appear as wrapped D4-branes
graphics grabbed from Sugimoto 16
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)
Last revised on May 8, 2025 at 16:43:57. See the history of this page for a list of all contributions to it.