Type IIB Killing spinors and calibrations

TL;DR

This paper derives differential equations for p-forms from type IIB Killing spinors, enabling the study of brane calibrations in supersymmetric backgrounds, with applications to giant gravitons in AdS_5 x S^5.

Contribution

It provides the full set of equations for p-forms in general type IIB backgrounds, facilitating the analysis of brane calibrations and stability conditions.

Findings

Derived differential equations for p-forms in type IIB backgrounds

Constructed calibration forms for giant gravitons in AdS_5 x S^5

Showed giant gravitons minimize energy minus momentum.

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''.