Waves on Mazes

TL;DR

This paper constructs new supersymmetric solutions describing M2-M5 brane systems with added momentum, revealing a linear structure that advances understanding of black hole entropy in supergravity.

Contribution

It introduces a method to add momentum to a complex M2-M5 brane system without altering the background, using linear equations, simplifying the analysis of black hole microstates.

Findings

Momentum excitations are governed by linear equations.

The solutions are parameterized by arbitrary functions of a null direction.

This approach advances the use of supergravity in black hole entropy calculations.

Abstract

One way to describe the entropy of black holes comes from partitioning momentum charge across fractionated intersecting brane systems. Here we construct $\frac{1}{8}$-BPS solutions by adding momentum to a maze of M2-brane strips stretched between M5 branes. Before the addition of momentum, the $\frac{1}{4}$-BPS supergravity solution describing the maze is governed by a master function obeying a complicated Monge-Amp\`ere equation. Given such a solution, we show that one can add momentum waves without modifying the $\frac{1}{4}$-BPS M2-M5 background. Remarkably, these excitations are fully determined by a layered set of $\textit{linear}$ equations. The fields responsible for carrying the momentum are parameterized by arbitrary functions of a null direction, and have exactly the same structure as in brane world-volume constructions. The fact that the momentum and flux excitations of the M2-M5-P system are governed by a linear structure brings us one step closer to using supergravity solutions to capture the entropy of supersymmetric black-holes.