A harmonic family of dielectric flow solutions with maximal supersymmetry

TL;DR

This work constructs a broad, analytically tractable family of maximally supersymmetric eleven-dimensional supergravity solutions describing M2 branes polarizing into M5 branes via a dielectric, harmonic flow. The construction relies on Killing-spinor techniques and a linear master function g, whose combination h = u^{-2}v^{-2}g is harmonic on ${\mathbb R}^8$, yielding a solvable PDE-based framework that generates the full metric and fluxes. Key results include the AdS$_4\times S^7$ UV asymptotics perturbed by mass deformations, the precise M2→M5 polarization into shells with calculable $N_5$ and shell radius $R_0$, and a detailed probe analysis showing a moduli space for polarized configurations that disappears unless M2 charge is present on the M5. The work provides a concrete resolution to the giant graviton puzzle within M-theory, clarifies when unpolarized coincident-brane backgrounds are physical, and offers a path to exploring dual Type IIB constructions and phase transitions in polarized-brane vacua.

Abstract

We construct a new harmonic family: dielectric flow solutions with maximal supersymmetry in eleven-dimensional supergravity. These solutions are asymptotically AdS_4 x S^7, while in the infra-red the M2 branes are dielectrically polarized into M5 branes. These solutions are holographically dual to vacua of the mass deformed theory on M2 branes. They also provide an interesting insight on the supergravity solutions sourced by giant gravitons, allowing one to see how supergravity solves the giant graviton puzzle.