# Chiral algebras, localization and surface defects

## Abstract

Four-dimensional N = 2 superconformal quantum field theories contain a subsector carrying the structure of a chiral algebra. Using localization techniques, we show for the free hypermultiplet that this structure can be accessed directly from the path integral on the four-sphere. We extend the localization computation to include supersymmetric surface defects described by a generic 4d/2d coupled system. The presence of a defect corresponds to considering a module of the chiral algebra: our results provide a calculational window into its structure constants.

- Authors:

- Uppsala Univ. (Sweden). Dept. of Physics and Astronomy
- Rutgers Univ., Piscataway, NJ (United States). New High Energy Theory Center

- Publication Date:

- Research Org.:
- Rutgers Univ., Piscataway, NJ (United States); Uppsala Univ. (Sweden)

- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25); Swedish Research Council (SRC); Knut and Alice Wallenberg Foundation (Sweden)

- OSTI Identifier:
- 1502377

- Grant/Contract Number:
- SC0010008; 2014-5517

- 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: 2; 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; extended supersymmetry; supersymmetry and duality

### Citation Formats

```
Pan, Yiwen, and Peelaers, Wolfger. Chiral algebras, localization and surface defects. United States: N. p., 2018.
Web. doi:10.1007/jhep02(2018)138.
```

```
Pan, Yiwen, & Peelaers, Wolfger. Chiral algebras, localization and surface defects. United States. doi:10.1007/jhep02(2018)138.
```

```
Pan, Yiwen, and Peelaers, Wolfger. Thu .
"Chiral algebras, localization and surface defects". United States. doi:10.1007/jhep02(2018)138. https://www.osti.gov/servlets/purl/1502377.
```

```
@article{osti_1502377,
```

title = {Chiral algebras, localization and surface defects},

author = {Pan, Yiwen and Peelaers, Wolfger},

abstractNote = {Four-dimensional N = 2 superconformal quantum field theories contain a subsector carrying the structure of a chiral algebra. Using localization techniques, we show for the free hypermultiplet that this structure can be accessed directly from the path integral on the four-sphere. We extend the localization computation to include supersymmetric surface defects described by a generic 4d/2d coupled system. The presence of a defect corresponds to considering a module of the chiral algebra: our results provide a calculational window into its structure constants.},

doi = {10.1007/jhep02(2018)138},

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

number = 2,

volume = 2018,

place = {United States},

year = {2018},

month = {2}

}

Free Publicly Available Full Text

Publisher's Version of Record

Other availability

Cited by: 7 works

*Citation information provided by*

Web of Science

Web of Science

Save to My Library

You must Sign In or Create an Account in order to save documents to your library.

Works referenced in this record:

##
Infinite Chiral Symmetry in Four Dimensions

journal, January 2015

- Beem, Christopher; Lemos, Madalena; Liendo, Pedro
- Communications in Mathematical Physics, Vol. 336, Issue 3

##
Higgs branch localization of N $$ \mathcal{N} $$ = 1 theories on S 3 × S 1

journal, August 2014

- Peelaers, Wolfger
- Journal of High Energy Physics, Vol. 2014, Issue 8

##
Vector two-point functions in maximally symmetric spaces

journal, December 1986

- Allen, Bruce; Jacobson, Theodore
- Communications in Mathematical Physics, Vol. 103, Issue 4

##
Elliptic Genera of 2d $${\mathcal{N}}$$ N = 2 Gauge Theories

journal, November 2014

- Benini, Francesco; Eager, Richard; Hori, Kentaro
- Communications in Mathematical Physics, Vol. 333, Issue 3

##
Topological quantum field theory

journal, September 1988

- Witten, Edward
- Communications in Mathematical Physics, Vol. 117, Issue 3

##
Semichiral fields on S 2 and generalized Kähler geometry

journal, January 2016

- Benini, Francesco; Crichigno, P. Marcos; Jain, Dharmesh
- Journal of High Energy Physics, Vol. 2016, Issue 1

##
Deformation Quantization and Superconformal Symmetry in Three Dimensions

journal, February 2017

- Beem, Christopher; Peelaers, Wolfger; Rastelli, Leonardo
- Communications in Mathematical Physics, Vol. 354, Issue 1

##
Gauge theory dynamics and Kähler potential for Calabi-Yau complex moduli

journal, December 2013

- Doroud, Nima; Gomis, Jaume
- Journal of High Energy Physics, Vol. 2013, Issue 12

##
Superconformal indices of generalized Argyres-Douglas theories from 2d TQFT

journal, February 2016

- Song, Jaewon
- Journal of High Energy Physics, Vol. 2016, Issue 2

##
Gauge Theories and Macdonald Polynomials

journal, November 2012

- Gadde, Abhijit; Rastelli, Leonardo; Razamat, Shlomo S.
- Communications in Mathematical Physics, Vol. 319, Issue 1

##
A topologically twisted index for three-dimensional supersymmetric theories

journal, July 2015

- Benini, Francesco; Zaffaroni, Alberto
- Journal of High Energy Physics, Vol. 2015, Issue 7

##
Schur indices, BPS particles, and Argyres-Douglas theories

journal, January 2016

- Córdova, Clay; Shao, Shu-Heng
- Journal of High Energy Physics, Vol. 2016, Issue 1

##
Long multiplet bootstrap

journal, October 2017

- Cornagliotto, Martina; Lemos, Madalena; Schomerus, Volker
- Journal of High Energy Physics, Vol. 2017, Issue 10

##
Infrared computations of defect Schur indices

journal, November 2016

- Córdova, Clay; Gaiotto, Davide; Shao, Shu-Heng
- Journal of High Energy Physics, Vol. 2016, Issue 11

##
Exact Kähler potential from gauge theory and mirror symmetry

journal, April 2013

- Gomis, Jaume; Lee, Sungjay
- Journal of High Energy Physics, Vol. 2013, Issue 4

##
5d Higgs branch localization, Seiberg-Witten equations and contact geometry

journal, January 2015

- Pan, Yiwen
- Journal of High Energy Physics, Vol. 2015, Issue 1

##
W $$ \mathcal{W} $$ symmetry in six dimensions

journal, May 2015

- Beem, Christopher; Rastelli, Leonardo; van Rees, Balt C.
- Journal of High Energy Physics, Vol. 2015, Issue 5

##
Chiral algebras for trinion theories

journal, February 2015

- Lemos, Madalena; Peelaers, Wolfger
- Journal of High Energy Physics, Vol. 2015, Issue 2

##
Surface defect indices and 2d-4d BPS states

journal, December 2017

- Córdova, Clay; Gaiotto, Davide; Shao, Shu-Heng
- Journal of High Energy Physics, Vol. 2017, Issue 12

##
Surface defects and chiral algebras

journal, May 2017

- Córdova, Clay; Gaiotto, Davide; Shao, Shu-Heng
- Journal of High Energy Physics, Vol. 2017, Issue 5

##
Ellipsoid partition function from Seiberg-Witten monopoles

journal, October 2015

- Pan, Yiwen; Peelaers, Wolfger
- Journal of High Energy Physics, Vol. 2015, Issue 10

##
Partition Functions of $${\mathcal{N}=(2,2)}$$ N = ( 2 , 2 ) Gauge Theories on S 2 and Vortices

journal, July 2014

- Benini, Francesco; Cremonesi, Stefano
- Communications in Mathematical Physics, Vol. 334, Issue 3

##
Intersecting surface defects and instanton partition functions

journal, July 2017

- Pan, Yiwen; Peelaers, Wolfger
- Journal of High Energy Physics, Vol. 2017, Issue 7

##
Exact correlators of BPS Operators from the 3d superconformal bootstrap

journal, March 2015

- Chester, Shai M.; Lee, Jaehoon; Pufu, Silviu S.
- Journal of High Energy Physics, Vol. 2015, Issue 3

##
Higgs branch localization in three dimensions

journal, May 2014

- Benini, Francesco; Peelaers, Wolfger
- Journal of High Energy Physics, Vol. 2014, Issue 5

##
The relationship between monopole harmonics and spin‐weighted spherical harmonics

journal, May 1985

- Dray, Tevian
- Journal of Mathematical Physics, Vol. 26, Issue 5

##
Rigid supersymmetric theories in curved superspace

journal, June 2011

- Festuccia, Guido; Seiberg, Nathan
- Journal of High Energy Physics, Vol. 2011, Issue 6

##
Argyres-Douglas theories, the Macdonald index, and an RG inequality

journal, February 2016

- Buican, Matthew; Nishinaka, Takahiro
- Journal of High Energy Physics, Vol. 2016, Issue 2

##
Elliptic Genera of Two-Dimensional $${\mathcal{N} = 2}$$ N = 2 Gauge Theories with Rank-One Gauge Groups

journal, November 2013

- Benini, Francesco; Eager, Richard; Hori, Kentaro
- Letters in Mathematical Physics, Vol. 104, Issue 4

##
Exact results in D = 2 supersymmetric gauge theories

journal, May 2013

- Doroud, Nima; Gomis, Jaume; Le Floch, Bruno
- Journal of High Energy Physics, Vol. 2013, Issue 5

##
The equivariant A-twist and gauged linear sigma models on the two-sphere

journal, June 2015

- Closset, Cyril; Cremonesi, Stefano; Park, Daniel S.
- Journal of High Energy Physics, Vol. 2015, Issue 6

##
Localization of Gauge Theory on a Four-Sphere and Supersymmetric Wilson Loops

journal, May 2012

- Pestun, Vasily
- Communications in Mathematical Physics, Vol. 313, Issue 1

##
Chiral algebras of class S $$ \mathcal{S} $$

journal, May 2015

- Beem, Christopher; Peelaers, Wolfger; Rastelli, Leonardo
- Journal of High Energy Physics, Vol. 2015, Issue 5

##
Dirac monopole without strings: Monopole harmonics

journal, May 1976

- Wu, Tai Tsun; Yang, Chen Ning
- Nuclear Physics B, Vol. 107, Issue 3

##
Stress-tensor OPE in N = 2 $$ \mathcal{N}=2 $$ superconformal theories

journal, February 2016

- Liendo, Pedro; Ramírez, Israel; Seo, Jihye
- Journal of High Energy Physics, Vol. 2016, Issue 2

##
On irregular singularity wave functions and superconformal indices

journal, September 2017

- Buican, Matthew; Nishinaka, Takahiro
- Journal of High Energy Physics, Vol. 2017, Issue 9

##
Liouville Correlation Functions from Four-Dimensional Gauge Theories

journal, January 2010

- Alday, Luis F.; Gaiotto, Davide; Tachikawa, Yuji
- Letters in Mathematical Physics, Vol. 91, Issue 2

##
Localization of the four-dimensional $ \mathcal{N}=4 $ SYM to a two-sphere and 1/8 BPS Wilson loops

journal, December 2012

- Pestun, Vasily
- Journal of High Energy Physics, Vol. 2012, Issue 12

##
Correlation functions of Coulomb branch operators

journal, January 2017

- Gerchkovitz, Efrat; Gomis, Jaume; Ishtiaque, Nafiz
- Journal of High Energy Physics, Vol. 2017, Issue 1

Works referencing / citing this record:

##
Schur correlation functions on S3 × S1

journal, July 2019

- Pan, Yiwen; Peelaers, Wolfger
- Journal of High Energy Physics, Vol. 2019, Issue 7