Argyres-Douglas theories, chiral algebras and wild Hitchin characters

2017/01/31 by Laura Fredrickson, Du Pei, Wenbin Yan +1 · 1 citation
Mathematics · Physics and Astronomy · #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #Mathematical physics #Particle physics #Physics #Quantum electrodynamics #Theoretical physics #hep-th #math-ph #math.AG #math.MP #math.QA #math.RT

paper · pdf · doi:10.1007/jhep01(2018)150

47+20 pages, 3 figures. v2: reference added, misprints corrected. v3: added corrections according to journal referee

openalex publication_date 2018/01/01 · arxiv created 2018/05/06 · arxiv updated 2018/05/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We use Coulomb branch indices of Argyres-Douglas theories on S1 × L(k, 1) to quantize moduli spaces M_H of wild/irregular Hitchin systems. In particular, we obtain formulae for the “wild Hitchin characters” — the graded dimensions of the Hilbert spaces from quantization — for four infinite families of M_H , giving access to many interesting geometric and topological data of these moduli spaces. We observe that the wild Hitchin characters can always be written as a sum over fixed points in M_H under the U(1) Hitchin action, and a limit of them can be identified with matrix elements of the modular transform ST k S in certain two-dimensional chiral algebras. Although naturally fitting into the geometric Langlands program, the appearance of chiral algebras, which was known previously to be associated with Schur operators but not Coulomb branch operators, is somewhat surprising.

Citations

• The Self-Duality Equations on a Riemann Surface
• Wild Harmonic Bundles and Wild Pure Twistor D-modules
• Lectures on the Langlands Program and Conformal Field Theory
• Geometric constraints on the space of N=2 SCFTs I: physical constraints on relevant deformations
• Mirror symmetry, Langlands duality, and the Hitchin system
• Electric-magnetic duality and the geometric Langlands program
• Factorisation and holomorphic blocks in 4d
• Twisted wild character varieties
• The Verlinde formula for Higgs bundles
• The equivariant Verlinde formula on the moduli of Higgs bundles
• Argyres-Douglas matter and N=2 dualities
• Quantization via Mirror Symmetry
• Topological reduction of 4D SYM to 2D σ-models
• Equivariant Verlinde Formula from Fivebranes and Vortices

Cited by

• Rozansky-Witten geometry of Coulomb branches and logarithmic knot invariants