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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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Before answering, please see our policy on resource recommendation questions. Please write substantial answers that detail the style, content, and prerequisites of the book, paper or other resource. Explain the nature of the resource so that readers can decide which one is best suited for them rather than relying on the opinions of others. Answers containing only a reference to a book or paper will be removed!

  • $\begingroup$ 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? $\endgroup$ – Mozibur Ullah Jan 18 '18 at 12:16
  • $\begingroup$ Have you come across Nlab? - they are a mine of information. $\endgroup$ – Mozibur Ullah Jan 18 '18 at 12:37
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Some useful information on the subject could be found in the paper by Manfred Herbst "On Higher Rank Coisotropic A-branes", but it is not exhaustive, so the question is still relevant.

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