1/8 BPS States in Ads/CFT

TL;DR

The paper addresses constructing fully backreacted 1/8 BPS states in AdS/CFT by extending bubbling techniques to a less supersymmetric sector. It develops a metric/5-form Ansatz preserving $SO(4)\times SU(2)\times U(1)$ symmetry and expresses the solution in terms of four scalars $m,n,p,T$ on a 3D half-space, constrained by nonlinear elliptic PDEs; an asymptotic analysis recovers the $AdS_5\times S^5$ background and identifies two KK charges $Q$ and $J$ associated with Cartan $U(1)$s of the $SO(6)$ isometry. The authors verify a BPS mass formula $M = (\pi L^2 / 4 G_5)(|J|+2|Q|)$ in the large-radius regime, while noting that a complete global mapping to boundary data at $y=0$ requires further work. The results connect 1/8 BPS bulk geometries to specific chiral primaries in the ${\cal N}=4$ SYM spectrum and lay groundwork for quantizing the solution space and understanding singularity resolution in this sector. This framework broadens the holographic dictionary beyond half- and quarter-BPS sectors, offering a path to explore microstate structure for less supersymmetric configurations.

Abstract

We study a class of exact supersymmetric solutions of type IIB Supergravity. They have an SO(4) x SU(2) x U(1) isometry and preserve generically 4 of the 32 supersymmetries of the theory. Asymptotically AdS_5 x S^5 solutions in this class are dual to 1/8 BPS chiral operators which preserve the same symmetries in the N=4 SYM theory. They are parametrized by a set of four functions that satisfy certain differential equations. We analyze the solutions to these equations in a large radius asymptotic expansion: they carry charges with respect to two U(1) KK gauge fields and their mass saturates the expected BPS bound.