## Argyres-Douglas theories, chiral algebras and wild Hitchin characters

## Abstract

We use Coulomb branch indices of Argyres-Douglas theories on *S ^{1} × 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*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.

^{k}S- Authors:

- 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)

- Publication Date:

- Research Org.:
- California Inst. of Tech., Pasadena (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC)

- OSTI Identifier:
- 1499648

- Grant/Contract Number:
- SC0011632

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Journal of High Energy Physics (Online)

- Additional Journal Information:
- Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2018; Journal Issue: 1; Journal ID: ISSN 1029-8479

- Publisher:
- Springer Berlin

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Conformal Field Theory; Differential and Algebraic Geometry; Supersymmetry and Duality

### Citation Formats

```
Fredrickson, Laura, Pei, Du, Yan, Wenbin, and Ye, Ke. Argyres-Douglas theories, chiral algebras and wild Hitchin characters. United States: N. p., 2018.
Web. doi:10.1007/jhep01(2018)150.
```

```
Fredrickson, Laura, Pei, Du, Yan, Wenbin, & Ye, Ke. Argyres-Douglas theories, chiral algebras and wild Hitchin characters. United States. doi:10.1007/jhep01(2018)150.
```

```
Fredrickson, Laura, Pei, Du, Yan, Wenbin, and Ye, Ke. Sat .
"Argyres-Douglas theories, chiral algebras and wild Hitchin characters". United States. doi:10.1007/jhep01(2018)150. https://www.osti.gov/servlets/purl/1499648.
```

```
@article{osti_1499648,
```

title = {Argyres-Douglas theories, chiral algebras and wild Hitchin characters},

author = {Fredrickson, Laura and Pei, Du and Yan, Wenbin and Ye, Ke},

abstractNote = {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 STkS 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.},

doi = {10.1007/jhep01(2018)150},

journal = {Journal of High Energy Physics (Online)},

number = 1,

volume = 2018,

place = {United States},

year = {2018},

month = {1}

}