We show in the SU(1, 1)-covariant formulation that IIB supergravity allows the introduction of a doublet and a quadruplet of ten-form potentials. The Ramond-Ramond ten-form potential which is associated with the SO(32) Type I superstring is in the quadruplet. Our results are consistent with a recently proposed E 11 symmetry underlying string theory. For the reader's convenience we present the full supersymmetry and gauge transformations of all fields both in the manifestly SU(1, 1) covariant Einstein frame and in the real U(1) gauge fixed string frame.

The construction of supersymmetric invariant integrals is discussed in a superspace setting. The formalism is applied to D = 4, N = 4 SYM and used to construct the F 2 , F 4 and (F 5 + ∂ 2 F 4 ) terms in the effective action of coincident D-branes. The results are in agreement with those obtained by other methods. A simple derivation of the abelian ∂ 4 F 4 invariant is given and generalised to the non-abelian case. We also find some double-trace invariants. The invariants are interpreted in terms of superconformal multiplets: the F 2 and F 4 terms are given by one-half BPS multiplets, the (F 5 + ∂ 2 F 4 ) arises as a full superspace integral of the Konishi multiplet K and the abelian ∂ 4 F 4 term comes from integrating the fourth power of the field strength superfield. Counterparts of the abelian invariants are exhibited for the D = 6, (2, 0) tensor multiplet and the D = 3, N = 8 scalar multiplet. The method is also applied to D = 4, N = 8 supergravity. All invariants in the linearised theory (with SU (8) symmetry) which arise from partial superspace integrals are constructed.

We give a universal SL(2, R)-invariant expression for all IIB p-brane actions with p = −1, 1, 3, 5, 7, 9. The Wess-Zumino terms in the brane actions are determined by requiring (i) target space gauge invariance and (ii) the presence of a single Born-Infeld vector. We find that for p = 7 (p = 9) brane actions with these properties only exist for orbits that contain the standard D7-brane (D9-brane). We comment about the actions for the other orbits.

We show that IIA supergravity can be extended with two independent 10-form potentials. These give rise to a single BPS IIA 9-brane. We investigate the bosonic gauge algebra of both IIA and IIB supergravity in the presence of 10-form potentials and point out an intriguing relation with the symmetry algebra E 11 , which has been conjectured to be the underlying symmetry of string theory/M-theory.

We calculate the tensions of all half-supersymmetric nine-branes in IIB string theory. In particular, we point out the existence of a solitonic IIB ninebrane. We find that the D9-brane and its duality transformations parametrize a two-dimensional surface in a four-dimensional space.