# Superconformal index, BPS monodromy and chiral algebras

## Abstract

We show that specializations of the 4d *N* = 2 superconformal index labeled by an integer *N* is given by Tr *M*N where *M* is the Kontsevich-Soibelman monodromy operator for BPS states on the Coulomb branch. We provide evidence that the states enumerated by these limits of the index lead to a family of 2d chiral algebras *A _{N}*. This generalizes the recent results for the N = –1 case which corresponds to the Schur limit of the superconformal index. We show that this specialization of the index leads to the same integrand as that of the elliptic genus of compactification of the superconformal theory on

*S*

^{2}×

*T*

^{2}where we turn on 1/2

*N*units of U(1)

_{r}flux on

*S*

^{2}.

- Authors:

- Scuola Internazionale Superiore di Studi Avanzati, Trieste (Italy)
- Univ. of California, La Jolla, CA (United States). Dept. of Physics
- Harvard Univ., Cambridge, MA (United States). Jefferson Physical Lab.
- Harvard Univ., Cambridge, MA (United States). Jefferson Physical Lab. and Center for Mathematical Sciences and Applications; California Inst. of Technology (CalTech), Pasadena, CA (United States). Walter Burke Inst. for Theoretical Physics

- Publication Date:

- Research Org.:
- Univ. of California, San Diego, CA (United States)

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

- OSTI Identifier:
- 1504762

- Grant/Contract Number:
- SC0009919; PHY-1067976

- Resource Type:
- Journal Article: Accepted Manuscript

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

- Additional Journal Information:
- Journal Volume: 2017; Journal Issue: 11; 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; Supersymmetric Gauge Theory

### Citation Formats

```
Cecotti, Sergio, Song, Jaewon, Vafa, Cumrun, and Yan, Wenbin.
```*Superconformal index, BPS monodromy and chiral algebras*. United States: N. p., 2017.
Web. doi:10.1007/jhep11(2017)013.

```
Cecotti, Sergio, Song, Jaewon, Vafa, Cumrun, & Yan, Wenbin.
```*Superconformal index, BPS monodromy and chiral algebras*. United States. doi:10.1007/jhep11(2017)013.

```
Cecotti, Sergio, Song, Jaewon, Vafa, Cumrun, and Yan, Wenbin. Mon .
"Superconformal index, BPS monodromy and chiral algebras". United States. doi:10.1007/jhep11(2017)013. https://www.osti.gov/servlets/purl/1504762.
```

```
@article{osti_1504762,
```

title = {Superconformal index, BPS monodromy and chiral algebras},

author = {Cecotti, Sergio and Song, Jaewon and Vafa, Cumrun and Yan, Wenbin},

abstractNote = {We show that specializations of the 4d N = 2 superconformal index labeled by an integer N is given by Tr MN where M is the Kontsevich-Soibelman monodromy operator for BPS states on the Coulomb branch. We provide evidence that the states enumerated by these limits of the index lead to a family of 2d chiral algebras AN. This generalizes the recent results for the N = –1 case which corresponds to the Schur limit of the superconformal index. We show that this specialization of the index leads to the same integrand as that of the elliptic genus of compactification of the superconformal theory on S2 × T2 where we turn on 1/2N units of U(1)r flux on S2.},

doi = {10.1007/jhep11(2017)013},

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

issn = {1029-8479},

number = 11,

volume = 2017,

place = {United States},

year = {2017},

month = {11}

}

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