2019/07/31 by Christopher Beem, Carlo Meneghelli, Wolfger Peelaers +1 · 1 citation
Mathematics · Physics and Astronomy · #Algebraic number #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Coxeter group #Duality (order theory) #Field (mathematics) #Homotopy and Cohomology in Algebraic Topology #Instanton #Operator (biology) #Operator algebra #Parameterized complexity #Singularity #Vertex (graph theory) #hep-th
paper · pdf · doi:10.1007/s00220-020-03746-9
published as Commun. Math. Phys. 377, 2553-2578 (2020) · 30 pages; v2: minor typos corrected, published version
openalex created_date 2019/07/30 · openalex publication_date 2020/03/30 · arxiv created 2020/04/17 · arxiv updated 2020/07/13 · openalex updated_date 2026/08/06
Abstract We analyze the \mathcal N=2 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>N</mml:mi> <mml:mo>=</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> 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.