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 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.
- 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)
- 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. https://doi.org/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. https://doi.org/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 = {Tue Sep 04 00:00:00 EDT 2018},
month = {Tue Sep 04 00:00:00 EDT 2018}
}
Web of Science
Figures / Tables:
Works referenced in this record:
ABCD of Instantons
journal, September 2004
- Nekrasov, Nikita; Shadchin, Sergey
- Communications in Mathematical Physics, Vol. 252, Issue 1-3
The 't Hooft–Polyakov monopole in the presence of a 't Hooft operator
journal, January 2009
- Cherkis, Sergey A.; Durcan, Brian
- Physics Letters B, Vol. 671, Issue 1
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
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
Toric reduction and a conjecture of Batyrev and Materov
journal, December 2004
- Szenes, András; Vergne, Michèle
- Inventiones mathematicae, Vol. 158, Issue 3
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
Seiberg-Witten Prepotential from Instanton Counting
journal, January 2003
- Nekrasov, Nikita A.
- Advances in Theoretical and Mathematical Physics, Vol. 7, Issue 5
Supersymmetric Boundary Conditions in $\mathcal{N}=4$ Super Yang-Mills Theory
journal, February 2009
- Gaiotto, Davide; Witten, Edward
- Journal of Statistical Physics, Vol. 135, Issue 5-6
Superconformal index with duality domain wall
journal, October 2012
- Gang, Dongmin; Koh, Eunkyung; Lee, Kimyeong
- Journal of High Energy Physics, Vol. 2012, Issue 10
Type IIB superstrings, BPS monopoles, and three-dimensional gauge dynamics
journal, May 1997
- Hanany, Amihay; Witten, Edward
- Nuclear Physics B, Vol. 492, Issue 1-2
$S$-duality of boundary conditions in ${\mathcal N}=4$ super Yang-Mills theory
journal, January 2009
- Gaiotto, David; Witten, Edward
- Advances in Theoretical and Mathematical Physics, Vol. 13, Issue 3
Darboux coordinates, Yang-Yang functional, and gauge theory
journal, July 2011
- Nekrasov, N.; Rosly, A.; Shatashvili, S.
- Nuclear Physics B - Proceedings Supplements, Vol. 216, Issue 1
Singular monopoles via the Nahm transform
journal, April 2008
- Cherkis, Sergey A.; Durcan, Brian
- Journal of High Energy Physics, Vol. 2008, Issue 04
Instantons on the Taub-NUT Space
journal, January 2010
- Cherkis, Sergey A.
- Advances in Theoretical and Mathematical Physics, Vol. 14, Issue 2
D-branes, monopoles and Nahm equations
journal, October 1997
- Diaconescu, Duiliu-Emanuel
- Nuclear Physics B, Vol. 503, Issue 1-2
Electric-magnetic duality and the geometric Langlands program
journal, January 2007
- Kapustin, Anton; Witten, Edward
- Communications in Number Theory and Physics, Vol. 1, Issue 1
General instanton counting and 5d SCFT
journal, July 2015
- Hwang, Chiung; Kim, Joonho; Kim, Seok
- Journal of High Energy Physics, Vol. 2015, Issue 7
Branes, instantons, and Taub-NUT spaces
journal, June 2009
- Witten, Edward
- Journal of High Energy Physics, Vol. 2009, Issue 06
Equivariant Volumes of Non-Compact Quotients and Instanton Counting
journal, May 2008
- Martens, Johan
- Communications in Mathematical Physics, Vol. 281, Issue 3
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
Singular monopoles and supersymmetric gauge theories in three dimensions
journal, August 1998
- Cherkis, Sergey A.; Kapustin, Anton
- Nuclear Physics B, Vol. 525, Issue 1-2
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
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
Magnetic monopole dynamics, supersymmetry, and duality
journal, January 2007
- Weinberg, Erick J.; Yi, Piljin
- Physics Reports, Vol. 438, Issue 2-4
Instantons on Gravitons
journal, June 2011
- Cherkis, Sergey A.
- Communications in Mathematical Physics, Vol. 306, Issue 2
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
Fusion rules and modular transformations in 2D conformal field theory
journal, January 1988
- Verlinde, Erik
- Nuclear Physics B, Vol. 300
Singular monopoles from Cheshire bows
journal, April 2011
- Blair, Chris D. A.; Cherkis, Sergey A.
- Nuclear Physics B, Vol. 845, Issue 1
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
Five-dimensional gauge theories and relativistic integrable systems
journal, October 1998
- Nekrasov, Nikita
- Nuclear Physics B, Vol. 531, Issue 1-3
Localization for nonabelian group actions
journal, April 1995
- Jeffrey, Lisa C.; Kirwan, Frances C.
- Topology, Vol. 34, Issue 2
A simple formalism for the BPS monopole
journal, March 1980
- Nahm, W.
- Physics Letters B, Vol. 90, Issue 4
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
Issues in topological gauge theory
journal, November 1998
- Losev, A.; Nekrasov, N.; Shatashvili, S.
- Nuclear Physics B, Vol. 534, Issue 3
Integrating over Higgs Branches
journal, January 2000
- Moore, Gregory; Nekrasov, Nikita; Shatashvili, Samson
- Communications in Mathematical Physics, Vol. 209, Issue 1
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
$${\mathcal{N} = 2}$$ 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
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
Witten index and wall crossing
journal, January 2015
- Hori, Kentaro; Kim, Heeyeon; Yi, Piljin
- Journal of High Energy Physics, Vol. 2015, Issue 1
Multi-instanton calculus on ALE spaces
journal, December 2004
- Fucito, Francesco; Morales, Jose F.; Poghossian, Rubik
- Nuclear Physics B, Vol. 703, Issue 3
Chern-Simons theory and S-duality
journal, May 2013
- Dimofte, Tudor; Gukov, Sergei
- Journal of High Energy Physics, Vol. 2013, Issue 5
Bound states of strings and p-branes
journal, February 1996
- Witten, Edward
- Nuclear Physics B, Vol. 460, Issue 2
Seiberg-Witten theories on ellipsoids
journal, September 2012
- Hama, Naofumi; Hosomichi, Kazuo
- Journal of High Energy Physics, Vol. 2012, Issue 9
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
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
Instanton counting on blowup. I. 4-dimensional pure gauge theory
journal, June 2005
- Nakajima, Hiraku; Yoshioka, Kota
- Inventiones mathematicae, Vol. 162, Issue 2
Saddle point equations in Seiberg-Witten theory
journal, October 2004
- Shadchin, Sergey
- Journal of High Energy Physics, Vol. 2004, Issue 10
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
Line operators on $ {S^{{1}}} \times {\mathbb{R}^{{3}}} $ and quantization of the Hitchin moduli space
journal, April 2012
- Ito, Yuto; Okuda, Takuya; Taki, Masato
- Journal of High Energy Physics, Vol. 2012, Issue 4
A Combinatorial Study on Quiver Varieties
journal, July 2017
- Fujii, Shigeyuki; Minabe, Satoshi
- Symmetry, Integrability and Geometry: Methods and Applications
Topology of the gauge condition and new confinement phases in non-abelian gauge theories
journal, October 1981
- Hooft, G. 't
- Nuclear Physics B, Vol. 190, Issue 3
A property of electric and magnetic flux in non-Abelian gauge theories
journal, January 1979
- 't Hooft, G.
- Nuclear Physics B, Vol. 153
On the phase transition towards permanent quark confinement
journal, June 1978
- 't Hooft, G.
- Nuclear Physics B, Vol. 138, Issue 1
Works referencing / citing this record:
Coulomb branch quantization and abelianized monopole bubbling
journal, October 2019
- Dedushenko, Mykola; Fan, Yale; Pufu, Silviu S.
- Journal of High Energy Physics, Vol. 2019, Issue 10
’t Hooft defects and wall crossing in SQM
journal, October 2019
- Brennan, T. Daniel; Dey, Anindya; Moore, Gregory W.
- Journal of High Energy Physics, Vol. 2019, Issue 10
On Monopole Bubbling Contributions to 't Hooft Loops
text, January 2019
- Assel, Benjamin; Sciarappa, Antonio
- arXiv
't Hooft Defects and Wall Crossing in SQM
text, January 2018
- Brennan, T. Daniel; Dey, Anindya; Moore, Gregory W.
- arXiv
Quantum line defects and refined BPS spectra
journal, October 2019
- Cirafici, Michele
- Letters in Mathematical Physics, Vol. 110, Issue 3
Figures / Tables found in this record: