Abstract
We continue our program of mapping data of 4D mathcal{N}=2 superconformal field theories (SCFTs) onto observables of 2D chiral rational conformal field theories (RCFTs) by revisiting an infinite set of strongly coupled Argyres-Douglas (AD) SCFTs and their associated logarithmic 2D chiral algebras. First, we turn on discrete flavor fugacities (for continuous flavor symmetries) in a known correspondence between certain unrefined characters of these logarithmic theories and unrefined characters of a set of unitary 2D chiral RCFTs. Motivated by this discussion, we then study 4D Higgs branch renormalization group flows (i.e., flows activated by vevs for which only su(2)R ⊂ su(2)R × u(1)R is spontaneously broken) emanating from our AD theories from the point of view of the unitary 2D theories and find some surprises. In particular, we argue that certain universal pieces of the topological data underlying the 2D chiral algebra representations associated with the 4D infrared (IR) theory can be computed, via Galois conjugation, in the topological quantum field theory (TQFT) underlying the unitary ultraviolet (UV) chiral RCFT. The mapping of this topological data from UV to IR agrees with the fact that, in our theories, the moduli spaces we study consist of free hypermultiplets at generic points if and only if the UV TQFT is a theory of abelian anyons.
Highlights
Motivated by these ideas and a duality discussed in [9, 15, 20], we embarked on a program in [21] to relate the logarithmic theories that appear via the correspondence in [2]4 with a more special set of 2D theories: the unitary rational conformal field theories (RCFTs)
We turn on discrete flavor fugacities in a known correspondence between certain unrefined characters of these logarithmic theories and unrefined characters of a set of unitary 2D chiral RCFTs
We argue that certain universal pieces of the topological data underlying the 2D chiral algebra representations associated with the 4D infrared (IR) theory can be computed, via Galois conjugation, in the topological quantum field theory (TQFT) underlying the unitary ultraviolet (UV) chiral RCFT
Summary
Our primary theories of interest are the so-called (A1, Dp) theories with p ∈ Zodd. These are 4D SCFTs, sometimes called Argyres-Douglas theories, that have N = 2 chiral primaries of non-integer scaling dimension. This property guarantees that they cannot be constructed by standard N = 2 Lagrangians. The pattern for general N is similar: these theories are compactifications of the AN−1 6D (2, 0) theory on a CP1 with an irregular and “full” regular puncture This latter puncture supports an su(N ) flavor symmetry with level ks4ud(N ). We can again fully Higgs the regular puncture and obtain the following RG flow (where again we drop decoupled free hypermultiplets) to a theory with just an irregular puncture (ANN−1[p − N ], F ) → ANN−1[p − N ]. We can consider RG flows in which we only partially Higgs the regular puncture (and break the associated global symmetry group to some more general subgroup). In these cases, we can have more complicated theories in the IR.
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