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T. Wrase, A. van Proeyen, M. Tournoy, C. Roupec:
"Non-supersymmetric branes";
Journal Of High Energy Physics, 07 (2020), 189.

We discuss how to incorporate non-supersymmetric branes in compactifications of type II string theories. We particularly focus on flux compactifications on SU(3) × SU(3) structure manifolds to four dimensions, so that a linear N = 1 supersymmetry is spontaneously broken by spacetime filling Dp-branes. Anti-Dp-branes are a very special subset of such branes but our analysis is generic. We show that the backreaction of non-supersymmetric branes can be incorporated into the standard 4d N = 1 supergravity by including a nilpotent chiral multiplet. Supersymmetry in such setups is always spontaneously broken and non-linearly realized. In particular this means that, contrary to what was previously thought, brane supersymmetry breaking cannot be simply described by a D-term in 4d N = 1 supergravity theories.

http://dx.doi.org/10.1007/JHEP07(2020)189