Holographic duals of five-dimensional SCFTs on a Riemann surface

TL;DR

This work constructs holographic $AdS_4$ duals for three-dimensional SCFTs obtained from twisted compactifications of five-dimensional Seiberg SCFTs on Riemann surfaces. By modeling the low-energy worldvolume theory of D4-branes wrapped on the surface within an O8/D8 background, the authors realize the internal Calabi–Yau geometry as a sum of two line bundles over the surface, with the twist parameters encoded in their degrees. They derive a general $AdS_4$ setup in massive IIA, then obtain explicit constant-curvature solutions labeled by $(p,q)$ that satisfy flux quantization and geometric constraints, and compute observables such as the free energy, flavor central charges, and D2-brane operator dimensions, all displaying nontrivial twist dependence and the characteristic $N^{5/2}$ scaling tied to the five-dimensional origin. The results provide strong evidence for 3d SCFTs arising from 5d twisted compactifications and hint at a richer structure, potentially including a TQFT on the Riemann surface, with avenues for further exploration of punctures and broader twist sectors.

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.

Figures (1)

• Figure 1: The $z$ dependence of the free energy, for fixed $g$, $N$ and $n_0$, is plotted for $\kappa=-1$ (red and dot-dashed curve), for $\kappa=0$ (green and dashed curve), and for $\kappa=1$ (blue and solid curve). Even though $F_z$ is plotted as a continuous function of $z$, only quantized values of $z$ correspond to SCFTs, as given in \ref{['pqpar']} for fixed genus $g$.