Calibrations and Fayyazuddin-Smith Spacetimes

TL;DR

Addressing how calibrated worldvolume solitons source full supergravity spacetimes, the paper shows FS spacetimes admit generalized Kahler calibrations. It develops a covariant relation $g=H f\\bar{f}$ between the Kahler metric determinant and the warp factor and uses this to generate new families of M2- and M5-brane backgrounds built on higher-dimensional Kahler bases. It provides explicit constructions for M2 spacetimes with complex dimension $N$ ($N=2$--$5$) preserving $1/2^N$ supersymmetry and for M5 spacetimes with $\phi=\tfrac12\omega\wedge\omega$ preserving $1/8$ SUSY, including calibrating forms that are gauge-equivalent to the source fields. The results offer a calibration-centric framework for embedding calibrated worldvolume solitons into eleven-dimensional supergravity and hint at extensions to cycles in Calabi-Yau manifolds and other calibrated geometries.

Abstract

We show that a class of spacetimes introduced by Fayyazuddin and Smith to describe intersecting M5-branes admit a generalized Kahler calibration. Equipped with this understanding, we are able to construct spacetimes corresponding to further classes of calibrated $p$-brane world-volume solitons. We note that these classes of spacetimes also describe the fields of $p$-branes wrapping certain supersymmetric cycles of Calabi-Yau manifolds.