Type IIB Killing spinors and calibrations

In this paper we derive the full set of differential equations and somealgebraic relations for p-forms constructed from type IIB Killing spinors.These equations are valid for the most general type IIB supersymmetricbackgrounds which have a non-zero NS-NS 3-form field strength, H, and non-zeroR-R field strengths, G^{(1)}, G^{(3)} and G^{(5)}. Our motivation is to usethese equations to obtain generalised calibrations for branes in supersymmetricbackgrounds. In particular, we consider giant gravitons in AdS_5 x S^5. Thesenon-static branes have an interesting construction via holomorphic surfaces inC^{1,2} x C^3. We construct the p-forms corresponding to these branes and showthat they satisfy the correct differential equations. Moreover, we interpretthe equations as calibration conditions and derive the calibration bound. Wefind that giant gravitons minimise ``energy minus momentum''.Comment: 26 pages, no figures; v2 some minor corrections and changes of sign for consistency of conventions, references added; v3 equations added for dual form