A bstract We investigate the admissible vector-valued modular forms having three independent characters and vanishing Wronskian index and determine which ones correspond to genuine 2d conformal field theories. This is done by finding bilinear coset-type relations that pair them into meromorphic characters with central charges 8, 16, 24, 32 and 40. Such pairings allow us to identify some characters with definite CFTs and rule out others. As a key result we classify all unitary three-character CFT with vanishing Wronskian index, excluding c = 8, 16. The complete list has two infinite affine series B r ,1 , D r ,1 and 45 additional theories. As a by-product, at higher values of the total central charge we also find constraints on the existence or otherwise of meromorphic theories. We separately list several cases that potentially correspond to Intermediate Vertex Operator Algebras.
VOAs and Rank-Two Instanton SCFTs
We analyze the N = 2 superconformal field theories that arise when a pair
of D3-branes probe an F-theory singularity from the perspective of the associated vertex operator algebra. We identify these vertex operator algebras for all cases; we find that they have a completely uniform description, parameterized by the dual Coxeter number of the corresponding global symmetry group. We further present free field realizations for these algebras in the style of recent work by three of the authors. These realizations transparently reflect the algebraic structure of the Higgs branches of these theories. We find fourth-order linear modular differential equations for the vacuum characters/Schur indices of these theories, which are again uniform across the full family of theories and parameterized by the dual Coxeter number.We comment briefly on expectations for the still higher-rank cases.
- Award ID(s):
- 1915093
- Publication Date:
- NSF-PAR ID:
- 10164110
- Journal Name:
- Communications in Mathematical Physics
- ISSN:
- 0010-3616
- Sponsoring Org:
- National Science Foundation
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- Publisher's Version of Record
- https://doi.org/10.1007/s00220-020-03746-9
