Holographic duals of five-dimensional SCFTs on a Riemann surface

TL;DR

This paper explores the holographic duals of five-dimensional SCFTs compactified on Riemann surfaces, constructing explicit AdS4 solutions in massive IIA supergravity and analyzing their physical properties.

Contribution

It provides the first explicit construction of AdS4 solutions dual to twisted compactifications of 5D SCFTs on Riemann surfaces, including detailed calculations of physical observables.

Findings

AdS4 solutions with N^{5/2} scaling in free energy

Dependence of operator dimensions on twist parameters

Evidence for the existence of 3D SCFTs from 5D origins

Abstract

We study the twisted compactifications of five-dimensional Seiberg SCFTs, with $SU_\mathcal{M}(2)\times E_{N_f+1}$ flavor symmetry, on a generic Riemann surface that preserves four supercharges. The five-dimensional SCFTs are obtained from the decoupling limit of $N$ D4-branes probing a geometry of $N_f<8$ D8-branes and an O8-plane. In addition to the R-symmetry, we can also twist the flavor symmetry by turning on background flux on the Riemann surface. In particular, in the string theory construction of the five-dimensional SCFTs, the background flux for the $SU_\mathcal{M}(2)$ has a geometric origin, similar to the topological twist of the R-symmetry. We argue that the resulting low-energy three-dimensional theories describe the dynamics on the world-volume of the $N$ D4-branes wrapped on the Riemann surface in the O8/D8 background. The Riemann surface can be described as a curve in a Calabi-Yau three-fold that is a sum of two line bundles over it. This allows for an explicit construction of $AdS_4$ solutions in massive IIA supergravity dual to the world-volume theories, thereby providing strong evidence that the three-dimensional SCFTs exist in the low-energy limit of the compactification of the five-dimensional SCFTs. We compute observables such as the free energy and the scaling dimensions of operators dual to D2-brane probes; these have non-trivial dependence on the twist parameter for the $U(1)$ in $SU_\mathcal{M}(2)$. The free energy exhibits the $N^{5/2}$ scaling that is emblematic of five-dimensional SCFTs.