A bstract There is a wellknown map from 4d $$ \mathcal{N} $$ N = 2 superconformal field theories (SCFTs) to 2d vertex operator algebras (VOAs). The 4d Schur index corresponds to the VOA vacuum character, and must be a solution with integral coefficients of a modular differential equation. This suggests a classification program for 4d $$ \mathcal{N} $$ N = 2 SCFTs that starts with modular differential equations and proceeds by imposing all known constraints that follow from the 4d → 2d map. This program becomes fully algorithmic once one specifies the order of the modular differential equation and the rank (complex dimension of the Coulomb branch) of the $$ \mathcal{N} $$ N = 2 theory. As a proof of concept, we apply the algorithm to the study of ranktwo $$ \mathcal{N} $$ N = 2 SCFTs whose Schur indices satisfy a fourthorder untwisted modular differential equation. Scanning over a large number of putative cases, only 15 satisfy all of the constraints imposed by our algorithm, six of which correspond to known 4d SCFTs. More sophisticated constraints can be used to argue against the existence of the remaining nine cases. Altogether, this indicates that our knowledge of such ranktwo SCFTsmore »
Deconfining $$ \mathcal{N} $$ = 2 SCFTs or the art of brane bending
A bstract We introduce a systematic approach to constructing $$ \mathcal{N} $$ N = 1 Lagrangians for a class of interacting $$ \mathcal{N} $$ N = 2 SCFTs. We analyse in detail the simplest case of the construction, arising from placing branes at an orientifolded ℂ 2 / ℤ 2 singularity. In this way we obtain Lagrangian descriptions for all the R 2 ,k theories. The rank one theories in this class are the E 6 MinahanNemeschansky theory and the C 2 × U(1) ArgyresWittig theory. The Lagrangians that arise from our brane construction manifestly exhibit either the entire expected flavour symmetry group of the SCFT (for even k ) or a fullrank subgroup thereof (for odd k ), so we can compute the full superconformal index of the $$ \mathcal{N} $$ N = 2 SCFTs, and also systematically identify the Higgsings associated to partial closing of punctures.
 Award ID(s):
 1914934
 Publication Date:
 NSFPAR ID:
 10377785
 Journal Name:
 Journal of High Energy Physics
 Volume:
 2022
 Issue:
 3
 ISSN:
 10298479
 Sponsoring Org:
 National Science Foundation
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