| Popis: |
We study gravitini zero modes in four dimensional N=2 pure supergravity theory. The gravitini zero modes we study are solutions to the Rarita-Schwinger equations of motion in the background of the purely bosonic Majumdar-Papapetrou background. We start with a very generic ansatz for the gravitini that involves 32 ansatz functions and reduce the Rarita-Schwinger equations to a set of linear coupled partial differential equations on R3: the kind familiar from electromagnetism with divergences, curls, etc. We first show how the gravitini zero modes due to broken supersymmetries arise in this setup and how they solve the equations on R3. Then we go on and obtain other solutions to these equations: the “extra” fermion zero modes, parametrized by four integration constants (one of the integration constants corresponds to the gravitini zero modes due to broken supersymmetries). A careful analysis of pure gauge solutions reveals that we have four independent extra zero modes. |
