Metastable supersymmetry breaking in image non-linear sigma-models Original Research Article

We perform a general study of the issue of metastability for supersymmetry-breaking vacua in theories with image and image global supersymmetry. This problem turns out to capture all the important qualitative features of the corresponding question in theories with local supersymmetry, where gravitational effects induce only quantitative modifications. Moreover, it allows to directly compare the conditions arising in the image and image cases, since the latter becomes particular case of the former in the rigid limit. Our strategy consists in a systematic investigation of the danger of instability coming from the sGoldstini scalars, whose masses are entirely due to supersymmetry breaking mass-splitting effects. We start by reviewing the metastability conditions arising in general image non-linear sigma-models with chiral and vector multiplets. We then turn to the case of general image non-linear sigma-models with hyper and vector multiplets. We first reproduce and clarify the known no-go theorems applying to theories with only Abelian vector multiplets and only hyper multiplets, and then derive new results applying to more general cases. To make the comparison with image models as clear as possible, we rely on a formulation of image models where one of the supersymmetries is manifestly realized in terms of ordinary superfields, whereas the other is realized through non-trivial transformations. We give a self-contained account of such a construction of image theories in image superspace, generalizing previous work on various aspects to reach a general and coordinate-covariant construction. We also present a direct computation of the supertrace of the mass matrix.