Non-Abelian R-symmetry and dielectric branes

TL;DR

This paper explores the holographic duals of R-symmetry operators in $ ext{AdS}_5 imes S^5$, focusing on dielectric effects and non-BPS branes, to better understand the non-BPS sector of $ ext{AdS}_5/ ext{CFT}_4$ correspondence.

Contribution

It introduces a novel interpretation of non-BPS branes as dielectric expansions of Kaluza-Klein monopoles, linking symmetry operators to boundary non-BPS branes in holography.

Findings

Non-BPS branes can be viewed as dielectric expansions of Kaluza-Klein monopoles.

Proposes symmetry theories and boundary operators for the $SO(6)_R$ symmetry.

Connects non-BPS branes to boundary symmetry operators in holographic duals.

Abstract

We study the holographic realization of the $SO(6)_R$ R-symmetry of $\mathcal{N}=4$ super Yang-Mills with unitary gauge group. Focusing on 1/2 BPS states in the $[0,J,0]$ representation of $SO(6)_R$, it is known that depending on the scaling of $J$ with $N$, these are best described holographically in terms of gravitational waves ($J\ll N$) or D3 brane giant gravitons ($J\sim N$). These two descriptions are bridged by the dielectric effect, as the D3 giant can be regarded as a puffed-up configuration of gravitational waves. The natural non-BPS branes for symmetry operators are either 4-branes or non-BPS Kaluza-Klein monopoles. We show that the former can be regarded as a dielectric expansion of the latter, in parallel to the charged operators. We also propose symTh and symTFT candidates for the $SO(6)_R$ symmetry, whose operators at the boundary must correspond to the non-BPS branes.