Tree unitarity in broken supergravity: (I). Single gravitino amplitude

Abstract

Tree unitarity is studied in a spontaneously broken N=1 supergravity theory containing nonabelian gauge interactions through the high energy behaviour of the amplitude for the reaction gauge boson + gauge boson → gaugino + gravitino. The leading energy dependence expected naively, gets cancelled through super-current conservation. The subleading energy growth survives and leads to a unitarity violation at a critical c.m. energy E_cr ~ 96πg⁻¹κ⁻¹m_3/2(m_g̅−2m_3/2)⁻¹. The requirement E_cr ≳κ⁻¹ imposes an upper bound m_gm⁻¹_3/2≲2+96πg⁻¹ on the gauginogravi tino mass ratio.