A Target superspace formulation and constraints

In this appendix, I very briefly mention the superspace formulation for 𝒩 = 2 type IIA [136Jump To The Next Citation Point] and IIB [309Jump To The Next Citation Point] and 𝒩 = 1 d = 11 [153Jump To The Next Citation Point, 117Jump To The Next Citation Point] supergravity theories. The first goal is to set the relevant notation for the superfield components describing the physical massless fields coupling to the brane effective action degrees of freedom described in the main text. These are the physical fields appearing in the standard component formulation of these theories, i.e., 11-dimensional supergravity [154Jump To The Next Citation Point], its dimensional reduction [233] and type IIB [440, 309Jump To The Next Citation Point]. The second goal is to present the set of constraints satisfied by these superfields ensuring both formulations are on-shell equivalent. The latter are crucial to prove the kappa symmetry invariance of brane effective actions in curved backgrounds discussed in Section 3.5.

 A.1 𝒩 = 2 type IIA/B superspace
 A.2 𝒩 = 1d = 11 supergravity conventions

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