Holographic duals of five-dimensional SCFTs on a Riemann surface

Abstract

Abstract We study the twisted compactifications of five-dimensional Seiberg SCFTs, with S U ℳ 2 × E N f + 1 $$ {\mathrm{SU}}_{\mathrm{\mathcal{M}}}(2)\times {E}_{N_f}+1 $$ 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 SUℳ(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 AdS4 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 SUℳ(2). The free energy exhibits the N 5/2 scaling that is emblematic of five-dimensional SCFTs.

Keywords

• AdS-CFT Correspondence
• Brane Dynamics in Gauge Theories
• D-branes