# On ’t Hooft defects, monopole bubbling and supersymmetric quantum mechanics

## Abstract

We revisit the localization computation of the expectation values of ’t Hooft operators in N = 2* SU(N) theory on R ^{3} × S ^{1}. We show that the part of the answer arising from “monopole bubbling” on R ^{3} can be understood as an equivariant integral over a Kronheimer-Nakajima moduli space of instantons on an orbifold of C ^{2}. It can also be described as a Witten index of a certain supersymmetric quiver quantum mechanics with N = (4, 4) supersymmetry. The map between the defect data and the quiver quantum mechanics is worked out for all values of N. For the SU(2) theory, we compute several examples of these line defect expectation values using the Witten index formula and confirm that the expressions agree with the formula derived by Okuda, Ito and Taki. In addition, we present a Type IIB construction — involving D1-D3-NS5-branes — for monopole bubbling in N = 2* SU(N) SYM and demonstrate how the quiver quantum mechanics arises in this brane picture.

- Authors:

- Rutgers Univ., Piscataway, NJ (United States). NHETC. Dept. of Physics and Astronomy

- Publication Date:

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

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

- OSTI Identifier:
- 1502391

- Grant/Contract Number:
- SC0010008

- 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: 9; Journal ID: ISSN 1029-8479

- Publisher:
- Springer Berlin

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; D-branes; solitons monopoles and instantons; supersymmetric gauge theory; Wilson, ’t Hooft and Polyakov loops

### Citation Formats

```
Brennan, T. Daniel, Dey, Anindya, and Moore, Gregory W. On ’t Hooft defects, monopole bubbling and supersymmetric quantum mechanics. United States: N. p., 2018.
Web. doi:10.1007/jhep09(2018)014.
```

```
Brennan, T. Daniel, Dey, Anindya, & Moore, Gregory W. On ’t Hooft defects, monopole bubbling and supersymmetric quantum mechanics. United States. doi:10.1007/jhep09(2018)014.
```

```
Brennan, T. Daniel, Dey, Anindya, and Moore, Gregory W. Tue .
"On ’t Hooft defects, monopole bubbling and supersymmetric quantum mechanics". United States. doi:10.1007/jhep09(2018)014. https://www.osti.gov/servlets/purl/1502391.
```

```
@article{osti_1502391,
```

title = {On ’t Hooft defects, monopole bubbling and supersymmetric quantum mechanics},

author = {Brennan, T. Daniel and Dey, Anindya and Moore, Gregory W.},

abstractNote = {We revisit the localization computation of the expectation values of ’t Hooft operators in N = 2* SU(N) theory on R3 × S1. We show that the part of the answer arising from “monopole bubbling” on R3 can be understood as an equivariant integral over a Kronheimer-Nakajima moduli space of instantons on an orbifold of C2. It can also be described as a Witten index of a certain supersymmetric quiver quantum mechanics with N = (4, 4) supersymmetry. The map between the defect data and the quiver quantum mechanics is worked out for all values of N. For the SU(2) theory, we compute several examples of these line defect expectation values using the Witten index formula and confirm that the expressions agree with the formula derived by Okuda, Ito and Taki. In addition, we present a Type IIB construction — involving D1-D3-NS5-branes — for monopole bubbling in N = 2* SU(N) SYM and demonstrate how the quiver quantum mechanics arises in this brane picture.},

doi = {10.1007/jhep09(2018)014},

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

number = 9,

volume = 2018,

place = {United States},

year = {2018},

month = {9}

}

*Citation information provided by*

Web of Science

Web of Science

#### Figures / Tables:

^{2}/Z

_{$n$}. Each node denotes the unitary group with the labelled rank. The circular nodes denote gauge groups and the square nodes denote the avour symmetries.

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Figures / Tables found in this record:

*Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.*