Warped Supersymmetry Breaking

We address the size of supersymmetry-breaking effects within string theory settings where the observable sector resides deep within a strongly warped region, with supersymmetry breaking not necessarily localized in that region. Our particular interest is in how the supersymmetry-breaking scale seen by the observable sector depends on this warping. We focus concretely on type IIB flux compactifications and obtain this dependence in two ways: by computing within the microscopic string theory supersymmetry-breaking masses in Dp-brane supermultiplets; and by investigating how warping gets encoded into masses within the low-energy 4D effective theory. We identify two different ways to identify `the' 4D gravitino in such systems—the state whose supersymmetry is the least broken, and the state whose couplings are the most similar to the 4D graviton's—and argue that these need not select the same state in strongly warped settings. We formulate the conditions required for the existence of a description in terms of a 4D SUGRA formulation, or in terms of 4D SUGRA together with soft-breaking terms, and describe in particular situations where neither exist for some non-supersymmetric compactifications. We suggest that some effects of warping are captured by a linear A dependence in the Kahler potential. We outline some implications of our results for the KKLT scenario of moduli stabilization with broken SUSY.