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Abstract
We study the partial breaking of N=2 rigid supersymmetry for a generic rigid special geometry of n abelian vector multiplets in the presence of Fayet–Iliopoulos terms induced by the hyper-Kähler momentum map. By exhibiting the symplectic structure of the problem we give invariant conditions for the breaking to occur, which rely on a quartic invariant of the Fayet–Iliopoulos charges as well as on a modification of the N=2 rigid symmetry algebra by a vector central charge.
Highlights
It is well known that partial breaking of rigid and local supersymmetry can occur [1,2], provided one evades [3,4,5,6,7,8,9,10,11] some no-go theorems [12,13,2] which are satisfied by a certain class of theories
Hughes and Polchinski first pointed out the possibility to realize partial breaking of global supersymmetry [5] and, in four dimensional gauge theories, this was realized for a model of a self-interacting N = 2 vector multiplet, in the presence of N = 2 electric and magnetic Fayet–Iliopoulos terms [8]
This model is closely connected to the Goldstone action of partially broken N = 2 supersymmetry [14] by integrating out the (N = 1) chiral-multiplets components of the N = 2 vector multiplet [15], reproducing the supersymmetric Born–Infeld action [16,17]
Summary
It is well known that partial breaking of rigid and local supersymmetry can occur [1,2], provided one evades [3,4,5,6,7,8,9,10,11] some no-go theorems [12,13,2] which are satisfied by a certain class of theories. Multi-field versions which generalize the supersymmetric Born– Infeld theory to an arbitrary number of vector multiplets were obtained, preserving N = 1 supersymmetry [15,18], or preserving a second non-linearly realized supersymmetry [19,20] It is the aim of the present note to further elucidate some general conditions for partial supersymmetry breaking to occur which are independent on the particular alignment of the unbroken supersymmetry with respect to the original two supersymmetries, and are independent of the particular representative of the Fayet–Iliopoulos charge vector which, in our problem, is a triplet of the N = 2 SU(2) R-symmetry and a symplectic vector with respect to the symplectic structure of the underlying Special Ge-.
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