# 5-branes in Topological String Theory (TST)

It is known that the topological A-model allows the existence of $\frac{1}{2} \left[ D + \mathrm{rank} \left( B \right) \right]$-dimensional branes, where $D$ is a dimensionality of spacetime, and $B$ is a B-field.

Witten showed that the A-model with the target space being the cotangent bundle $T^*M$ to some 3-fold $M$ is equivalent to the Chern-Simons theory defined on this space which is interpreted as an effective theory living on the stack of 3-branes wrapping the base $M$. More general 3-branes configurations are possible if these branes wrap a Lagrangian submanifold of the embedding space. Generically, in accordance to what stated above, 5-branes are also allowed in a CY 3-fold if one has a non-zero $B$-field.

Question: Could anybody recommend any literature on these higher-dimensional topological branes and their world volume theories?

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• I'm trying to grasp the basics of string theory and am struggling to conceptualise it physically. Is $M$ here, spacetime? Then a stack of 3-branes is ambiently spread throughout spacetime - this means that each brane is as large as spacetime, like a field. But a stack implies a separation, how can they then be separated in space? – Mozibur Ullah Jan 18 '18 at 12:16
• Have you come across Nlab? - they are a mine of information. – Mozibur Ullah Jan 18 '18 at 12:37