Argyres-Douglas theories, chiral algebras and wild Hitchin characters

Fredrickson, Laura; Pei, Du; Yan, Wenbin; Ye, Ke

doi:10.1007/jhep01(2018)150

Title: Argyres-Douglas theories, chiral algebras and wild Hitchin characters

Journal Article · 19 January 2018 · Journal of High Energy Physics (Online)

DOI: https://doi.org/10.1007/jhep01(2018)150 · OSTI ID:1499648

Fredrickson, Laura ^[1]; Pei, Du ^[2]; Yan, Wenbin ^[3]; Ye, Ke ^[4]

Stanford Univ., CA (United States); Stanford Univ., CA (United States)
California Inst. of Tech., Pasadena (United States); Univ. of Aarhus, Aarhus (Denmark)
Tsinghua Univ., Beijing (China); Harvard Univ., Cambridge, MA (United States)
California Inst. of Tech., Pasadena (United States)

We use Coulomb branch indices of Argyres-Douglas theories on S¹ × L(k,1) to quantize moduli spaces $$\mathcal{M}$$_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 $$\mathcal{M}$$_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 $$\mathcal{M}$$_H under the U(1) Hitchin action, and a limit of them can be identified with matrix elements of the modular transform ST^kS 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.

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Research Organization:: California Inst. of Technology (CalTech), Pasadena, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)

Grant/Contract Number:: SC0011632

OSTI ID:: 1499648

Journal Information:: Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 1 Vol. 2018; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

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