Type IIB Killing spinors and calibrations

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 × S 5 . These non-static branes have an interesting construction via holomorphic surfaces in C 1,2 ×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".

Symmetric backgrounds of type IIB supergravity

“…The most general invariant rank-r form in this space has the form 9) where the first term is the wedge product of the Cahen-Wallach volume form with an invariant form on as riemannian factor, the second term is an invariant form on a riemannian factor, and the third term is a sum of wedge products of Cahen-Wallach non-volume invariant forms and invariant forms on riemannian factors. Using that the τ i are null, the norm squared of W (r) is 10) whereas the inner interior product in the transverse directions of the Cahen-Wallach part is…”

“…However, we know that solutions exist for AdS 2 × S 2 × S 2 × S 2 × T 2 and AdS 2 × S 2 × S 2 × H 2 × T 2 as limits of the solutions for AdS 2 × S 4 × S 2 × T 2 and AdS 2 × S 4 × H 2 × T 2 . 12,10), for a total of 38 parameters. The resultant system of polynomials does not lend itself to symbolic solution.…”

“…In [10] (see also [2]) it is shown that the Killing vectors constructed out of Killing spinors preserve C (0) , whence the recent proof [4] of the strong homogeneity conjecture implies that any type IIB backgrounds preserving more than one half of the supersymmetry are strongly homogeneous.…”

BPS electromagnetic waves on giant gravitons

“…Especially supersymmetric giant gravitons extended in S q were characterized by the intersection of S q and a holomorphic surface by Mikhailov [5]. See also [6,7]. Giant graviton as an extended D-brane could in principle carry dynamical world-volume gauge field, still keeping supersymmetry.…”

Central charges of wrapped M5-brane backgrounds

“…The analysis has been further generalised to include arbitrary supersymmetric backgrounds and worldvolume fields in eleven [6] and ten [7] dimensions. These topological charges of the algebra indicate what supersymmetric brane probes are possible in the chosen background, and also what possible relevance to the corresponding worldvolume gauge theory they might have.…”