Exceptional N=6 and N=2 AdS ₄ supergravity, and zero-center modules

We study the gauging of the orthosymplectic algebras OSp(6|4) × SO(2) and its ''dual'' OSp(2|4) × SO(6), both based on supergravities with the same exceptional coset SO*(12)/U(6), and gauge group SO(6) × SO(2). The two dual theories are obtained by two different truncations of gauged = 8 AdS ₄ supergravity. We explicitly study the gauge sector of the two dual theories with the most general group allowed by supersymmetry. The = 6 gravity multiplet has also the exceptional property to be a zero-center module of OSp(6|4), as it is the case for superconformal Yang-Mills theory in four dimensions based on SU(2,2|n) (PSU(2,2|4) for n = 4) or OSp(n|4).