Gauged Six-dimensional Supergravity from Massive Type IIA

We obtain the complete non-linear Kaluza-Klein ansatz for the reduction of the bosonic sector of massive type IIA supergravity to the Romans F(4) gauged supergravity in six dimensions. The latter arises as a consistent warped S^4 reduction.Comment: Latex, 7 page

Anti-de Sitter space, branes, singletons, superconformal field theories and all that

There has recently been a revival of interest in anti de-Sitter space (AdS) brought about by the conjectured duality beteeen physics in the bulk of AdS and a conformal field theory on the boundary. Since the whole subject of branes, singletons and superconformal field theories on the AdS boundary was an active area of research about ten years ago, I begin with a historical review, including the ``Membrane at the end of the universe'' idea. Next I discuss two recent papers with Lu and Pope on on $AdS_{5} \times S^{5}$ and on $AdS_{3} \times S^{3}$, respectively. In each case we note that odd-dimensional spheres $S^{{2n+1}}$ may be regarded as U(1) bundles over $CP^{n}$ and that this permits an unconventional ``Hopf''duality along the U(1) fibre. This leads in particular to the phenomenon of BPS without BPS whereby states which appear to be non-BPS in one picture are seen to be BPS in the dual picture.Comment: Minor improvements. 37 pages Latex. Based on talks delivered at the the PASCOS 98 conference, Northeastern University, March 1998; the Superfivebranes and Physics in 5+1 Dimensions conference, ICTP, Trieste, Italy, April 1998; the Arnowitt Fest, Texas A&M University, April 1998; the Strings 98 conference, ITP, Santa Barbara, June 199

Spectrum of D=6, N=4b Supergravity on AdS_3 x S^3

The complete spectrum of D=6, N=4b supergravity with n tensor multiplets compactified on AdS_3 x S^3 is determined. The D=6 theory obtained from the K_3 compactification of Type IIB string requires that n=21, but we let n be arbitrary. The superalgebra that underlies the symmetry of the resulting supergravity theory in AdS_3 coupled to matter is SU(1,1|2)_L x SU(1,1|2)_R. The theory also has an unbroken global SO(4)_R x SO(n) symmetry inherited from D=6. The spectrum of states arranges itself into a tower of spin-2 supermultiplets, a tower of spin-1, SO(n) singlet supermultiplets, a tower of spin-1 supermultiplets in the vector representation of SO(n) and a special spin-1/2 supermultiplet also in the vector representation of SO(n). The SU(2)_L x SU(2)_R Yang-Mills states reside in the second level of the spin-2 tower and the lowest level of the spin-1, SO(n) singlet tower and the associated field theory exhibits interesting properties.Comment: 37 pages, latex, 5 tables and 3 figures, typos corrected, a reference adde