That's a wrap!

TL;DR

This work broadens the calibration toolkit for M-theory by introducing a general rule for generalized calibrations in flux backgrounds, enabling the construction of supergravity solutions for M-branes wrapped on holomorphic cycles beyond Kahler settings. By linking calibrations to metric constraints and providing a concise shortcut, it unifies M2 and M5 wrapped-brane solutions and reproduces known results (FS1/FS2) while revealing non-Kahler calibrations. The approach is demonstrated through explicit examples (M2 on 2-cycles, M5 on 2- and 4-cycles) and is shown to have limitations, notably for certain higher-dimensional holomorphic cycles (e.g., M5 on 4-cycles in C^4). The work significantly expands the landscape of accessible BPS configurations in flux backgrounds and points to rich future directions in identifying additional calibrations.

Abstract

Calibration technology provides us with a fast and elegant way to find the supergravity solutions for BPS wrapped M-branes. Its true potential had however remained untapped due to the absence of a classification of calibrations in spacetimes with non-trivial flux. The applications of this method were thus limited in practise to M-branes wrapping Kahler calibrated cycles. In this paper, we catagorize a type of generalised calibrations which exist in supergravity backgrounds and contain Kahler calibrations as a sub-class. This broadens the arena of brane configurations whose supergravity solutions are accessible through the calibration 'short-cut' method.