Bulk charges in eleven dimensions

TL;DR

This paper explores how relaxing boundary conditions in eleven-dimensional supergravity allows for static solutions with non-zero bulk charges, leading to new black hole representations and insights into membrane decay processes.

Contribution

It introduces generalized boundary conditions in eleven-dimensional supergravity that enable static solutions with bulk charges and examines their implications for black hole and membrane physics.

Findings

Bulk charge can be non-zero under relaxed boundary conditions.

New static solutions preserve 1/16 to 1/4 of supersymmetries.

Dimensional reduction yields novel four-dimensional black hole solutions.

Abstract

Eleven dimensional supergravity has electric type currents arising from the Chern-Simon and anomaly terms in the action. However the bulk charge integrates to zero for asymptotically flat solutions with topological trivial spatial sections. We show that by relaxing the boundary conditions to generalisations of the ALE and ALF boundary conditions in four dimensions one can obtain static solutions with a bulk charge preserving between 1/16 and 1/4 of the supersymmetries. One can introduce membranes with the same sign of charge into these backgrounds. This raises the possibility that these generalized membranes might decay quantum mechanically to leave just a bulk distribution of charge. Alternatively and more probably, a bulk distribution of charge can decay into a collection of singlely charged membranes. Dimensional reductions of these solutions lead to novel representations of extreme black holes in four dimensions with up to four charges. We discuss how the eleven-dimensional Kaluza-Klein monopole wrapped around a space with non-zero first Pontryagin class picks up an electric charge proportional to the Pontryagin number.