Reading Chern-Simons Theory, Matrix Models, and Topological Strings by Marcos Marino, I'm trying to understand the argument in 7.3.2: here are my main questions which can also be seen as some general string theory questions.

1. Why is the string field theory description of the open B-model topological string called a "spacetime description?" By SUSY localization, the action is $$S = \int_X \Omega \wedge \mathrm{Tr} (A \wedge \bar{\partial} A + \frac{2}{3} A \wedge A \wedge A) $$ where the string field $A$ is just a $\mathrm{End} (E)$ valued 1 form (vector bundle connection) on spacetime $X$. So is it a "spacetime description" just because we have recognized the degrees of freedom of the open string theory as a spacetime QFT?

On the other hand, I understand that in string theory, the usual idea is that the massless part of the spectrum of open strings ending on some d-branes is identified as the spectrum of a worldvolume qft which is some Yang-Mills type theory; what is the relation of that YM theory with the string field A?

2. In particular, in a case with some $N$ d-branes, we have "the spacetime description can be obtained by considering the dimensional reduction of the original string field theory (above action). As usual in D-brane physics, the gauge potential splits into a gauge potential on the world volume of the brane and Higgs fields describing the motion along non-compact, transverse directions." Can someone clarify what is going on here? This is reminiscent of the usual SSB argument with d-brane field theory, but having trouble piecing it together.

Reading the book$^{\dagger}$ Chern-Simons Theory, Matrix Models, and Topological Strings by Marcos Marino, I'm trying to understand the argument in 7.3.2: here are my main questions which can also be seen as some general string theory questions.

1. Why is the string field theory description of the open B-model topological string called a "spacetime description?" By SUSY localization, the action is $$S = \int_X \Omega \wedge \mathrm{Tr} (A \wedge \bar{\partial} A + \frac{2}{3} A \wedge A \wedge A) $$ where the string field $A$ is just a $\mathrm{End} (E)$ valued 1 form (vector bundle connection) on spacetime $X$. So is it a "spacetime description" just because we have recognized the degrees of freedom of the open string theory as a spacetime QFT?

On the other hand, I understand that in string theory, the usual idea is that the massless part of the spectrum of open strings ending on some d-branes is identified as the spectrum of a worldvolume qft which is some Yang-Mills type theory; what is the relation of that YM theory with the string field A?

2. In particular, in a case with some $N$ d-branes, we have "the spacetime description can be obtained by considering the dimensional reduction of the original string field theory (above action). As usual in D-brane physics, the gauge potential splits into a gauge potential on the world volume of the brane and Higgs fields describing the motion along non-compact, transverse directions." Can someone clarify what is going on here? This is reminiscent of the usual SSB argument with D-brane field theory, but having trouble piecing it together.

${}^{\dagger}$ There is an arXiv version: https://arxiv.org/abs/hep-th/0410165. See 3.3 in particular.