Electrostatic Description of Five-dimensional SCFTs

TL;DR

This work develops an electrostatic-like description of a broad family of AdS$_6$ backgrounds in Type IIB supergravity, dual to five-dimensional ${\cal N}=1$ SCFTs with linear quivers. A single potential $V(\sigma,\eta)$ solving a linear PDE governs the full geometry and fluxes; the boundary Rank function ${\cal R}(\eta)$ encodes the quiver data, including gauge ranks $N_k$ and flavor content. The authors compute the holographic central charge $c_{hol}$ and Wilson loop VEVs, showing precise agreement with field-theory results in the large quiver limit and providing explicit examples (e.g., ${\tilde T}_{N,P}$ and $+_{P,N}$ theories). Special solutions and dualities (Type IIA Abelian/NATD) are explored, clarifying the role of boundary conditions and the need for completion to obtain well-defined SCFT duals. Overall, the paper strengthens the link between convex Rank-function boundaries, quiver data, and holographic observables in AdS$_6$/5d SCFT holography.

Abstract

In this paper we discuss an infinite class of AdS$_6$ backgrounds in Type IIB supergravity dual to five dimensional SCFTs whose low energy description is in terms of linear quiver theories. The quantisation of the Page charges imposes that each solution is determined once a convex, piece-wise linear function is specified. In the dual field theory, we interpret this function as encoding the ranks of colour and flavour groups in the associated quiver. We check our proposal with several examples and provide general expressions for the holographic central charge and the Wilson loop VEV. Some solutions outside this general class, with less clear quiver interpretation, are also discussed.

Figures (1)

• Figure 1: Depiction of the electrostatic problem for $\widehat{V}$. The two conducting planes at $\eta=0,P$ have zero potential, while at $\sigma=0$ we have a charge distribution equal to $\cal R (\eta)$.