Electrostatic Description of Five-dimensional SCFTs

TL;DR

This paper introduces a class of Type IIB supergravity backgrounds dual to five-dimensional SCFTs, characterized by a convex piece-wise linear function encoding quiver gauge theory data, and provides holographic calculations of central charges and Wilson loops.

Contribution

It proposes a new geometric framework for describing 5d SCFTs via convex functions, linking supergravity solutions to quiver gauge theories and computing key physical quantities.

Findings

Explicit supergravity solutions for 5d SCFTs are constructed.

Holographic central charges and Wilson loop VEVs are derived.

Examples validate the proposed geometric-quiver correspondence.

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.