Worldvolume theories, holography, duality and time

Abstract

Duality transformations involving compactifications on timelike as well as spacelike circles link M-theory, the 10 +1-dimensional strong coupling limit of IIA string theory, to other 11-dimensional theories in signatures 9 +2 and 6 +5 and to type II string theories in all 10-dimensional signatures. These theories have BPS branes of various world-volume signatures, and here we construct the world-volume theories for these branes, which in each case have 16 supersymmetries. For the generalised D-branes of the various type II string theories, these are always supersymmetric Yang–Mills theories with 16 supersymmetries, and we show that these all arise from compactifications of the supersymmetric Yang–Mills theories in 9 +1 or 5 +5 dimensions. We discuss the geometry of the brane solutions and, for the cases in which the world-volume theories are superconformally invariant, we propose holographically dual string or M theories in constant curvature backgrounds. For product space solutions X×Y, there is in general a conformal field theory associated with the boundary of X and another with the boundary of Y.