2-branes with Arnold-Beltrami Fluxes from Minimal D=7 Supergravity

TL;DR

This paper uncovers a novel connection between Beltrami equations in hydrodynamics and minimal D=7 supergravity, revealing exact two-brane solutions with Arnold-Beltrami fluxes and implications for dual gauge theories.

Contribution

It demonstrates that only D=7 supergravity admits exact two-brane solutions with Arnold-Beltrami fluxes, linking hydrodynamic eigenfunctions to supergravity solutions.

Findings

Exact two-brane solutions with Arnold-Beltrami fluxes in D=7 supergravity

Discrete groups classify Beltrami eigenfunctions on a three-torus

Potential for new insights into dual three-dimensional gauge theories

Abstract

We describe this paper as a Sentimental Journey from Hydrodynamics to Supergravity. Beltrami equation in three dimensions that plays a key role in the hydrodynamics of incompressible fluids has an unsuspected relation with minimal supergravity in seven dimensions. We show that just D=7 supergravity and no other theory with the same field content but different coefficients in the lagrangian, admits exact two-brane solutions where Arnold-Beltrami fluxes in the transverse directions have been switched on. The rich variety of discrete groups that classify the solutions of Beltrami equation, namely the eigenfunctions of the *d operator on a three-torus, are by this newly discovered token injected into the brane world. A new quite extensive playing ground opens up for supergravity and for its dual gauge theories in three dimensions, where all classical fields and all quantum composite operators will be assigned to irreducible representations of discrete crystallographic groups.