Abstract
We study the twisted compactifications of five-dimensional Seiberg SCFTs, with {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 Nf < 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 N5/2 scaling that is emblematic of five-dimensional SCFTs.
Highlights
SCFTs carry an SUM(2) × ENf +1 flavor symmetry
We study the twisted compactifications of five-dimensional Seiberg SCFTs, with SUM(2) × ENf +1 flavor symmetry, on a generic Riemann surface that preserves four supercharges
We restrict to cases where the resulting three-dimensional quantum field theory preserves at least four supercharges; these are given by topological twists of the fivedimensional SCFTs [6, 7] on the Riemann surface
Summary
The field theory limit to a point on the Coulomb branch is gY2 M = fixed, φ = fixed, s → 0 This limit necessarily puts the D4-branes on the O8-plane where there is a USp(2N ) gauge symmetry. A constant spinor is obtained by turning on a background field to cancel the spin connection In effect this identifies the holonomy group of the curved geometry, in which ωμ is valued, with a subgroup of the R-symmetry. Unlike the coefficients of JR3 , the other twist parameters (z, zi) are not constrained by the topological twist Another way to understand these more general embeddings of the holonomy group is to consider the background gauge fields valued in the global symmetry. Our interest now is to argue that the three-dimensional field theories are SCFTs and the SO(1, 2) enhances to the superconformal group, SO(2, 3)
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