Non-static brane probes, topological charges and calibrations
In this thesis we consider probe branes in 10- and 11-dimensional supergravity backgrounds. Firstly, we consider probing a class of 11-dimensional backgrounds with giant gravitons. These backgrounds arise from lifting solutions of 4-dimensional U(1)(^4) and 7-dimensional U(1)(^2) gauged supergravities. We find that giant gravitons degenerate to massless particles exist in arbitrary lifted backgrounds, and furthermore both these objects are degenerate to massive charged particles probing the associated lower-dimensional gauged supergravity solutions. We then move on to consider superalgebras for M2- and M5-brane probes in general 11-dimensional supersymmetric backgrounds. We derive the form of the topological charges which appear in the super translation part of the algebra. These charges are given by the integral (over the spatial world-volume of the brane) of certain closed forms constructed from Killing spinors and background fields. The super- translation algebra allows us to derive BPS bounds on the energy/momentum of probe branes in these general supersymmetric backgrounds. These bounds can be interpreted as generalized calibration bounds for these branes. We then use a similar procedure in type IIB supergravity to construct a calibration bound for a giant graviton in AdS(^5) x S(^5). As a by-product of this construction, we find a number of differential and algebraic relations satisfied by p-forms constructed from Killing spinors in type IIB supergravity. These relations are valid for the most general supersymmetric backgrounds. We then show that the calibration bound which we have constructed is saturated by a large class of general giant gravitons in AdS(^5) x S(^5), which are defined via holomorphic surfaces in C(^1)'(^2) x C(^3). Moreover, dual giant gravitons also saturate the calibration bound. We find that both these branes minimize "energy minus momentum" in their homology class.