Couch-Torrence conformal inversion, supersymmetry and conserved charges for D3-branes

TL;DR

This paper explores the use of Couch-Torrence conformal inversion to connect asymptotic and near-horizon charges in D3-brane geometries, revealing new conserved quantities and their supersymmetric relations.

Contribution

It constructs and matches Newman-Penrose and Aretakis charges in higher-dimensional D3-brane geometries and relates scalar charges to higher spin charges via supersymmetry.

Findings

Established a precise matching between asymptotic and near-horizon charges via inversion.

Constructed infinite towers of conserved spinorial charges associated with dilatino fluctuations.

Demonstrated the relation between scalar dilaton charges and higher spin charges using supersymmetry.

Abstract

An asymptotically flat spacetime in $D=4$ can be mapped via Couch-Torrence conformal inversion to the geometry around an extremal non-expanding and non-rotating horizon. At the linearized level, an infinite tower of conserved Newman-Penrose charges can be found at null-infinity, while infinitely many Aretakis charges are conserved in the near-horizon. Couch-Torrence inversion allows one to establish a matching between the two sets of asymptotic charges. In this work we construct the Newman-Penrose and Aretakis scalar charges in higher-dimensional geometries of D3-branes in $D=10$ and D3-brane bound states in $D=4$ and $D=5$ and establish a precise matching between them through the inversion. By exploiting the residual unbroken supersymmetry of Type IIB supergravity, we demonstrate that it is possible to relate scalar (complex dilaton) charges to higher spin charges. In particular, we determine infinite towers of conserved asymptotic spinorial charges associated with the dilatino fluctuations, and determine the map through inversion.