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Title: 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:
 [1];  [1];  [1]
  1. 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}
}

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Cited by: 8 works
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Figures / Tables:

Figure 1 Figure 1: The Kronheimer-Nakajima quiver for a regular U(N) instantons on C2/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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Works referenced in this record:

ABCD of Instantons
journal, September 2004

  • Nekrasov, Nikita; Shadchin, Sergey
  • Communications in Mathematical Physics, Vol. 252, Issue 1-3
  • DOI: 10.1007/s00220-004-1189-1

The 't Hooft–Polyakov monopole in the presence of a 't Hooft operator
journal, January 2009


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
  • DOI: 10.1007/s00220-014-2210-y

5d gauge theories on orbifolds and 4d ’t Hooft line indices
journal, November 2013

  • Mekareeya, Noppadol; Rodríguez-Gómez, Diego
  • Journal of High Energy Physics, Vol. 2013, Issue 11
  • DOI: 10.1007/JHEP11(2013)157

Toric reduction and a conjecture of Batyrev and Materov
journal, December 2004


Parameter counting for singular monopoles on ℝ3
journal, October 2014

  • Moore, Gregory W.; Royston, Andrew B.; Van den Bleeken, Dieter
  • Journal of High Energy Physics, Vol. 2014, Issue 10
  • DOI: 10.1007/JHEP10(2014)142

Seiberg-Witten Prepotential from Instanton Counting
journal, January 2003


Supersymmetric Boundary Conditions in $\mathcal{N}=4$ Super Yang-Mills Theory
journal, February 2009


Superconformal index with duality domain wall
journal, October 2012

  • Gang, Dongmin; Koh, Eunkyung; Lee, Kimyeong
  • Journal of High Energy Physics, Vol. 2012, Issue 10
  • DOI: 10.1007/JHEP10(2012)187

Type IIB superstrings, BPS monopoles, and three-dimensional gauge dynamics
journal, May 1997


$S$-duality of boundary conditions in ${\mathcal N}=4$ super Yang-Mills theory
journal, January 2009


Darboux coordinates, Yang-Yang functional, and gauge theory
journal, July 2011


Singular monopoles via the Nahm transform
journal, April 2008


Instantons on the Taub-NUT Space
journal, January 2010


D-branes, monopoles and Nahm equations
journal, October 1997


Electric-magnetic duality and the geometric Langlands program
journal, January 2007


General instanton counting and 5d SCFT
journal, July 2015

  • Hwang, Chiung; Kim, Joonho; Kim, Seok
  • Journal of High Energy Physics, Vol. 2015, Issue 7
  • DOI: 10.1007/JHEP07(2015)063

Branes, instantons, and Taub-NUT spaces
journal, June 2009


Equivariant Volumes of Non-Compact Quotients and Instanton Counting
journal, May 2008


On instantons as Kaluza-Klein modes of M5-branes
journal, December 2011

  • Kim, Hee-Cheol; Kim, Seok; Koh, Eunkyung
  • Journal of High Energy Physics, Vol. 2011, Issue 12
  • DOI: 10.1007/JHEP12(2011)031

Singular monopoles and supersymmetric gauge theories in three dimensions
journal, August 1998


Brane bending and monopole moduli
journal, October 2014

  • Moore, Gregory W.; Royston, Andrew B.; Van den Bleeken, Dieter
  • Journal of High Energy Physics, Vol. 2014, Issue 10
  • DOI: 10.1007/JHEP10(2014)157

Exact results for ’t Hooft loops in Gauge theories on S 4
journal, May 2012

  • Gomis, Jaume; Okuda, Takuya; Pestun, Vasily
  • Journal of High Energy Physics, Vol. 2012, Issue 5
  • DOI: 10.1007/JHEP05(2012)141

Magnetic monopole dynamics, supersymmetry, and duality
journal, January 2007


Instantons on Gravitons
journal, June 2011


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
  • DOI: 10.1007/s11005-010-0369-5

Fusion rules and modular transformations in 2D conformal field theory
journal, January 1988


Singular monopoles from Cheshire bows
journal, April 2011


The Coulomb Branch of 3d $${\mathcal{N}= 4}$$ N = 4 Theories
journal, June 2017

  • Bullimore, Mathew; Dimofte, Tudor; Gaiotto, Davide
  • Communications in Mathematical Physics, Vol. 354, Issue 2
  • DOI: 10.1007/s00220-017-2903-0

Five-dimensional gauge theories and relativistic integrable systems
journal, October 1998


Localization for nonabelian group actions
journal, April 1995


A simple formalism for the BPS monopole
journal, March 1980


Loop and surface operators in $ \mathcal{N} = 2 $ gauge theory and Liouville modular geometry
journal, January 2010

  • Alday, Luis F.; Gaiotto, Davide; Gukov, Sergei
  • Journal of High Energy Physics, Vol. 2010, Issue 1
  • DOI: 10.1007/JHEP01(2010)113

Issues in topological gauge theory
journal, November 1998


Integrating over Higgs Branches
journal, January 2000

  • Moore, Gregory; Nekrasov, Nikita; Shatashvili, Samson
  • Communications in Mathematical Physics, Vol. 209, Issue 1
  • DOI: 10.1007/PL00005525

Line Operator Index on S 1 × S 3
journal, May 2012

  • Gang, Dongmin; Koh, Eunkyung; Lee, Kimyeong
  • Journal of High Energy Physics, Vol. 2012, Issue 5
  • DOI: 10.1007/JHEP05(2012)007

$${\mathcal{N} = 2}$$ N = 2 Quiver Gauge Theories on A-type ALE Spaces
journal, November 2014

  • Bruzzo, Ugo; Sala, Francesco; Szabo, Richard J.
  • Letters in Mathematical Physics, Vol. 105, Issue 3
  • DOI: 10.1007/s11005-014-0734-x

Gauge theory loop operators and Liouville theory
journal, February 2010

  • Drukker, Nadav; Gomis, Jaume; Okuda, Takuya
  • Journal of High Energy Physics, Vol. 2010, Issue 2
  • DOI: 10.1007/JHEP02(2010)057

Witten index and wall crossing
journal, January 2015

  • Hori, Kentaro; Kim, Heeyeon; Yi, Piljin
  • Journal of High Energy Physics, Vol. 2015, Issue 1
  • DOI: 10.1007/JHEP01(2015)124

Multi-instanton calculus on ALE spaces
journal, December 2004


Chern-Simons theory and S-duality
journal, May 2013


Bound states of strings and p-branes
journal, February 1996


Seiberg-Witten theories on ellipsoids
journal, September 2012


Semiclassical framed BPS states
journal, July 2016

  • Moore, Gregory W.; Royston, Andrew B.; Van den Bleeken, Dieter
  • Journal of High Energy Physics, Vol. 2016, Issue 7
  • DOI: 10.1007/JHEP07(2016)071

Localization of Gauge Theory on a Four-Sphere and Supersymmetric Wilson Loops
journal, May 2012


Instanton counting on blowup. I. 4-dimensional pure gauge theory
journal, June 2005


Saddle point equations in Seiberg-Witten theory
journal, October 2004


Lectures on 2D yang-mills theory, equivariant cohomology and topological field theories
journal, April 1995

  • Cordes, Stefan; Moore, Gregory; Ramgoolam, Sanjaye
  • Nuclear Physics B - Proceedings Supplements, Vol. 41, Issue 1-3
  • DOI: 10.1016/0920-5632(95)00434-B