Abstract
We initiate a study of the holographic duals of a class of four-dimensional mathcal{N} = 2 superconformal field theories that are engineered by wrapping M5-branes on a sphere with an irregular puncture. These notably include the strongly-coupled field theories of Argyres-Douglas type. Our solutions are obtained in 7d gauged supergravity, where they take the form of a warped product of AdS5 and a “half-spindle.” The irregular puncture is modeled by a localized M5-brane source in the internal space of the gravity duals. Our solutions feature a realization of supersymmetry that is distinct from the usual topological twist, as well as an interesting Stückelberg mechanism involving the gauge field associated to a generator of the isometry algebra of the internal space. We check the proposed duality by computing the holographic central charge, the flavor symmetry central charge, and the dimensions of various supersymmetric probe M2-branes, and matching these with the dual Argyres-Douglas field theories. Furthermore, we compute the large-N ’t Hooft anomalies of the field theories using anomaly inflow methods in M-theory, and find perfect agreement with the proposed duality.
Highlights
The Argyres-Douglas (AD) field theories have particular significance among fourdimensional N = 2 superconformal field theories (SCFTs)
We observe that the solutions admit a u(1)2 ⊕ su(2) isometry algebra, but the algebra of continuous (0-form) symmetries of the dual SCFTs is only u(1) ⊕ su(2), which is identified with the R-symmetry algebra of 4d N = 2 superconformal symmetry
We encounter an obstruction in the construction of E4, which is resolved by demonstrating that only one linear combination of the u(1)2 isometry generators translates to a continuous symmetry of the SCFT, with the other combination being spontaneously broken by a Stückelberg mechanism
Summary
In this paper we present the first gravity duals of AD theories in M-theory, and provide a new perspective on both the geometry of the irregular puncture and the curious field theoretic properties of these SCFTs. An important motivation to this work has been the recent work on branes wrapping spindle geometries1 [14, 15] as a novel way of preserving supersymmetry. This novel connection between irregular punctures and sources in supergravity paves the way to further investigations and generalizations to other brane constructions Another peculiar property of our solutions is related to the interplay between the isometry algebra of the internal space and the algebra of global zero-form symmetries in the SCFT. A brief summary of some results of the supergravity solutions and checks of the proposed duality were first reported in [27]
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