Type IIB Killing spinors and calibrations

TL;DR

The authors construct p-forms from Type IIB Killing spinors and derive their complete differential and algebraic relations in general SUSY backgrounds with $H$ and RR fluxes. They then specialize to giant gravitons in $AdS_5\times S^5$ via Mikhailov's holomorphic-surface construction, computing explicit forms and showing these satisfy the general equations, enabling a calibration interpretation. By modifying the calibration data to account for nonzero $G^{(5)}$, they obtain a calibration bound that holomorphic and dual giant gravitons saturate, effectively minimizing energy minus momentum in their homology class. The framework provides a robust, non-static-brane calibration approach in Type IIB backgrounds and has potential applications to background classification and broader non-static brane phenomena.

Abstract

In this paper we derive the full set of differential equations and some algebraic relations for p-forms constructed from type IIB Killing spinors. These equations are valid for the most general type IIB supersymmetric backgrounds which have a non-zero NS-NS 3-form field strength, H, and non-zero R-R field strengths, G^{(1)}, G^{(3)} and G^{(5)}. Our motivation is to use these equations to obtain generalised calibrations for branes in supersymmetric backgrounds. In particular, we consider giant gravitons in AdS_5 x S^5. These non-static branes have an interesting construction via holomorphic surfaces in C^{1,2} x C^3. We construct the p-forms corresponding to these branes and show that they satisfy the correct differential equations. Moreover, we interpret the equations as calibration conditions and derive the calibration bound. We find that giant gravitons minimise ``energy minus momentum''.