Half-BPS supergravity solutions and superalgebras

We establish a correspondence between certain Lie superalgebras with 16 fermionic generators, and half-BPS solutions to supergravities with 32 supersymmetries. Three cases are discussed. For Type IIB supergravity, we relate semi-simple Lie superalgebras H with 16 fermionic generators which are subalgebras of PSU(2, 2 vertical bar 4), to families of half-BPS solutions which are invariant under H, and locally asymptotic to AdS(5) x S-5. Similarly, for M-theory, we relate semi-simple Lie superalgebras H with 16 fermionic generators which are subalgebras of OSp(8*vertical bar 4) or OSp(8 vertical bar 4, R) to families of half-BPS solutions which are invariant under H, and locally asymptotic to AdS(7) x S-4 or AdS(4) x S-7 respectively. Possible enhancements to more than 16 supersymmetries, such as 24, are also analyzed. The classification of semi-simple subalgebras of PSU(2, 2 vertical bar 4), OSp(8*vertical bar 4), and OSp(8 vertical bar 4, R) derived in this paper, leads us to conjecture the existence of various new families of half-BPS solutions to Type IIB supergravity and M-theory.