# Branes wrapping curves in M-theory. What does it mean?

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1. What does it mean that a M5-branes wraps a holomorphic curve in M-theory? In specific a lot of Vafa's paper involve various branes (not only M5) wrapping some cycles.

2. What does this really mean intuitively and physically?

3. Also, when a brane intersects a compact divisor in a (non-compact) CY3-fold what does it physically mean?

This post imported from StackExchange Physics at 2015-05-06 11:15 (UTC), posted by SE-user Marion
Hard to tell if the question is after the basic concept or some subtleties of it. Let's first check if the basic concept is clear: a brane configuration of shape some manifold $\Sigma$ inside a target spacetime $X$ is a suitably well behaved map $\Sigma \to X$. One says that such a configuration wraps cycles in $X$ if it represents the corresponding element in the homology group of $X$. For instance if $\Sigma = T^2$and $X = Y \times T^2$ then the brane wraps that torus surface if the embedding map is the identity onto that torus over some point of $Y$.
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