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On irregular singularity wave functions and superconformal indices

We generalize, in a manifestly Weyl-invariant way, our previous expressions for irregular singularity wave functions in two-dimensional SU(2) q-deformed Yang-Mills theory to SU(N). As an application, we give closed-form expressions for the Schur indices of all (A N − 1 , A N (n − 1)−1) Argyres-Douglas (AD) superconformal field theories (SCFTs), thus completing the computation of...

\( \mathcal{N} \) = 2 S-duality revisited

Using the chiral algebra bootstrap, we revisit the simplest Argyres-Douglas (AD) generalization of Argyres-Seiberg S-duality. We argue that the exotic AD superconformal field theory (SCFT), \( {\mathcal{T}}_{3,\frac{3}{2}} \), emerging in this duality splits into a free piece and an interacting piece, \( {\mathcal{T}}_X \), even though this factorization seems invisible in the...

On 4d rank-one \( \mathcal{N}=3 \) superconformal field theories

We study the properties of 4d \( \mathcal{N}=3 \) superconformal field theories whose rank is one, i.e. those that reduce to a single vector multiplet on their moduli space of vacua. We find that the moduli space can only be of the form ℂ3/ℤ ℓ for ℓ=1, 2, 3, 4, 6, and that the supersymmetry automatically enhances to \( \mathcal{N}=4 \) for ℓ=1, 2. In addition, we determine the...

Argyres-Douglas theories, the Macdonald index, and an RG inequality

We conjecture closed-form expressions for the Macdonald limits of the super-conformal indices of the (A 1 , A 2n − 3) and (A 1 , D 2n ) Argyres-Douglas (AD) theories in terms of certain simple deformations of Macdonald polynomials. As checks of our conjectures, we demonstrate compatibility with two S-dualities, we show symmetry enhancement for special values of n, and we argue...

Compact conformal manifolds

In this note we begin a systematic study of compact conformal manifolds of SCFTs in four dimensions (our notion of compactness is with respect to the topology induced by the Zamolodchikov metric). Supersymmetry guarantees that such manifolds are Kähler, and so the simplest possible non-trivial compact conformal manifold in this set of geometries is a complex one-dimensional...

Affine SU(N) algebra from wall-crossings

Takahiro Nishinaka 1 Satoshi Yamaguchi 0 0 Department of Physics, Graduate School of Science, Osaka University , Toyonaka, Osaka 560-0043, Japan 1 High Energy Accelerator Research Organization (KEK

Constraints on chiral operators in \( \mathcal{N}=2 \) SCFTs

We study certain higher-spin chiral operators in \( \mathcal{N}=2 \) superconformal field theories (SCFTs). In Lagrangian theories, or in theories related to Lagrangian theories by generalized Argyres-Seiberg-Gaiotto duality (“type A” theories in our classification), we give a simple superconformal representation theory proof that such operators do not exist. This argument is...

Topological strings and 5d T N partition functions

We evaluate the Nekrasov partition function of 5d gauge theories engineered by webs of 5-branes, using the refined topological vertex on the dual Calabi-Yau three-folds. The theories include certain non-Lagrangian theories such as the T N theory. The refined topological vertex computation generically contains contributions from decoupled M2-branes which are not charged under the...

Two-dimensional crystal melting and D4-D2-D0 on toric Calabi-Yau singularities

We construct a two-dimensional crystal melting model which reproduces the BPS index of D2-D0 states bound to a non-compact D4-brane on an arbitrary toric CalabiYau singularity. The crystalline structure depends on the toric divisor wrapped by the D4-brane. The molten crystals are in one-to-one correspondence with the torus fixed points of the moduli space of the quiver gauge...

Argyres-Douglas theories and S-duality

We generalize S-duality to \( \mathcal{N}=2 \) superconformal field theories (SCFTs) with Coulomb branch operators of non-integer scaling dimension. As simple examples, we find minimal generalizations of the S-dualities discovered in SU(2) gauge theory with four fundamental flavors by Seiberg and Witten and in SU(3) gauge theory with six fundamental flavors by Argyres and Seiberg...