The Tensor Hierarchies of Pure N=2,d=4,5,6 Supergravities

We study the supersymmetric tensor hierarchy of pure (gauged) N=2,d=4,5,6 supergravity and compare them with those of the pure, ungauged, theories (worked out by Gomis and Roest for d=5) and the predictions of the Kac-Moody approach made by Kleinschmidt and Roest. We find complete agreement in the ungauged case but we also find that, after gauging, new Stueckelberg symmetries reduce the number of independent "physical" top-forms. The analysis has to be performed to all orders in fermion fields. We discuss the construction of the worldvolume effective actions for the p-branes which are charged with respect to the (p+1)-form potentials and the relations between the tensor hierarchies and p-branes upon dimensional reduction.Comment: LaTeX2e file, 20 pages, 1 figure Results refined by extension of the analysis to all orders in fermion

Holographic Renormalization for z=2 Lifshitz Space-Times from AdS

Lifshitz space-times with critical exponent z=2 can be obtained by dimensional reduction of Schroedinger space-times with critical exponent z=0. The latter space-times are asymptotically AdS solutions of AdS gravity coupled to an axion-dilaton system and can be uplifted to solutions of type IIB supergravity. This basic observation is used to perform holographic renormalization for 4-dimensional asymptotically z=2 locally Lifshitz space-times by Scherk-Schwarz dimensional reduction of the corresponding problem of holographic renormalization for 5-dimensional asymptotically locally AdS space-times coupled to an axion-dilaton system. We can thus define and characterize a 4-dimensional asymptotically locally z=2 Lifshitz space-time in terms of 5-dimensional AdS boundary data. In this setup the 4-dimensional structure of the Fefferman-Graham expansion and the structure of the counterterm action, including the scale anomaly, will be discussed. We find that for asymptotically locally z=2 Lifshitz space-times obtained in this way there are two anomalies each with their own associated nonzero central charge. Both anomalies follow from the Scherk--Schwarz dimensional reduction of the 5-dimensional conformal anomaly of AdS gravity coupled to an axion-dilaton system. Together they make up an action that is of the Horava-Lifshitz type with nonzero potential term for z=2 conformal gravity.Comment: 32 pages, v2: modified discussion of the central charge