Index-like theorems from line defect vevs

Brennan, T. Daniel; Moore, Gregory W.

doi:10.1007/jhep09(2019)073

Title: Index-like theorems from line defect vevs

Journal Article · 10 September 2019 · Journal of High Energy Physics (Online)

DOI: https://doi.org/10.1007/jhep09(2019)073 · OSTI ID:1611320

^[1]; Moore, Gregory W. ^[2]

Rutgers Univ., Piscataway, NJ (United States); DOE/OSTI
Rutgers Univ., Piscataway, NJ (United States)

In this paper we investigate the relation between complexified Fenchel-Nielsen coordinates and spectral network coordinates on Seiberg-Witten moduli space. The main technique is the comparison of exact expressions for the expectation value of ’t Hooft defects in certain 4D SU(2) N = 2 gauge theories. We derive an index-like theorem for a class of Dirac operators on singular monopole moduli spaces. Our expression determines the indices of Dirac operators on singular monopole moduli spaces in terms of characteristic numbers for vector bundles over certain Kronheimer-Nakajima quiver varieties.

View Accepted Manuscript (DOE)

Cite

Export

Save

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

Sponsoring Organization:: USDOE Office of Science (SC)

Grant/Contract Number:: SC0010008

OSTI ID:: 1611320

Journal Information:: Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 9 Vol. 2019; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

References (48)

Spectral networks Neitzke, Andy Banff International Research Station for Mathematical Innovation and Discovery https://doi.org/10.14288/1.0043279	audiovisual	January 2014
Bundles over Moduli Spaces and the Quantization of BPS Monopoles Manton, N. S.; Schroers, B. J. Annals of Physics, Vol. 225, Issue 2 https://doi.org/10.1006/aphy.1993.1060	journal	August 1993
Yang-Mills instantons on ALE gravitational instantons Kronheimer, Peter B.; Nakajima, Hiraku Mathematische Annalen, Vol. 288, Issue 1 https://doi.org/10.1007/BF01444534	journal	December 1990
Loop and surface operators in $ \mathcal{N} = 2 $ gauge theory and Liouville modular geometry Alday, Luis F.; Gaiotto, Davide; Gukov, Sergei Journal of High Energy Physics, Vol. 2010, Issue 1 https://doi.org/10.1007/JHEP01(2010)113	journal	January 2010
Gauge theory loop operators and Liouville theory Drukker, Nadav; Gomis, Jaume; Okuda, Takuya Journal of High Energy Physics, Vol. 2010, Issue 2 https://doi.org/10.1007/JHEP02(2010)057	journal	February 2010
ADE spectral networks and decoupling limits of surface defects Longhi, Pietro; Park, Chan Y. Journal of High Energy Physics, Vol. 2017, Issue 2 https://doi.org/10.1007/JHEP02(2017)011	journal	February 2017
Line operators on $ {S^{{1}}} \times {\mathbb{R}^{{3}}} $ and quantization of the Hitchin moduli space Ito, Yuto; Okuda, Takuya; Taki, Masato Journal of High Energy Physics, Vol. 2012, Issue 4 https://doi.org/10.1007/JHEP04(2012)010	journal	April 2012
Exact results for ’t Hooft loops in Gauge theories on S 4 Gomis, Jaume; Okuda, Takuya; Pestun, Vasily Journal of High Energy Physics, Vol. 2012, Issue 5 https://doi.org/10.1007/JHEP05(2012)141	journal	May 2012
Chern-Simons theory and S-duality Dimofte, Tudor; Gukov, Sergei Journal of High Energy Physics, Vol. 2013, Issue 5 https://doi.org/10.1007/JHEP05(2013)109	journal	May 2013
On monopole bubbling contributions to ’t Hooft loops Assel, Benjamin; Sciarappa, Antonio Journal of High Energy Physics, Vol. 2019, Issue 5 https://doi.org/10.1007/JHEP05(2019)180	journal	May 2019
Monopoles and Wilson lines Tong, David; Wong, Kenny Journal of High Energy Physics, Vol. 2014, Issue 6 https://doi.org/10.1007/JHEP06(2014)048	journal	June 2014
Semiclassical framed BPS states Moore, Gregory W.; Royston, Andrew B.; Van den Bleeken, Dieter Journal of High Energy Physics, Vol. 2016, Issue 7 https://doi.org/10.1007/JHEP07(2016)071	journal	July 2016
N = 2 dualities Gaiotto, Davide Journal of High Energy Physics, Vol. 2012, Issue 8 https://doi.org/10.1007/JHEP08(2012)034	journal	August 2012
ADE spectral networks Longhi, Pietro; Park, Chan Y. Journal of High Energy Physics, Vol. 2016, Issue 8 https://doi.org/10.1007/JHEP08(2016)087	journal	August 2016
On ’t Hooft defects, monopole bubbling and supersymmetric quantum mechanics Brennan, T. Daniel; Dey, Anindya; Moore, Gregory W. Journal of High Energy Physics, Vol. 2018, Issue 9 https://doi.org/10.1007/JHEP09(2018)014	journal	September 2018
Monopole bubbling via string theory Brennan, T. Daniel Journal of High Energy Physics, Vol. 2018, Issue 11 https://doi.org/10.1007/JHEP11(2018)126	journal	November 2018
Integrating over Higgs Branches Moore, Gregory; Nekrasov, Nikita; Shatashvili, Samson Communications in Mathematical Physics, Vol. 209, Issue 1 https://doi.org/10.1007/PL00005525	journal	January 2000
Spectral Networks and Snakes Gaiotto, Davide; Moore, Gregory W.; Neitzke, Andrew Annales Henri Poincaré, Vol. 15, Issue 1 https://doi.org/10.1007/s00023-013-0238-8	journal	March 2013
Spectral Networks Gaiotto, Davide; Moore, Gregory W.; Neitzke, Andrew Annales Henri Poincaré, Vol. 14, Issue 7 https://doi.org/10.1007/s00023-013-0239-7	journal	March 2013
Equivariant Volumes of Non-Compact Quotients and Instanton Counting Martens, Johan Communications in Mathematical Physics, Vol. 281, Issue 3 https://doi.org/10.1007/s00220-008-0501-x	journal	May 2008
Four-Dimensional Wall-Crossing via Three-Dimensional Field Theory Gaiotto, Davide; Moore, Gregory W.; Neitzke, Andrew Communications in Mathematical Physics, Vol. 299, Issue 1 https://doi.org/10.1007/s00220-010-1071-2	journal	July 2010
D -Particle Bound States and Generalized Instantons Moore, Gregory; Nekrasov, Nikita; Shatashvili, Samson Communications in Mathematical Physics, Vol. 209, Issue 1 https://doi.org/10.1007/s002200050016	journal	January 2000
Supersymmetric Boundary Conditions in $\mathcal{N}=4$ Super Yang-Mills Theory Gaiotto, Davide; Witten, Edward Journal of Statistical Physics, Vol. 135, Issue 5-6 https://doi.org/10.1007/s10955-009-9687-3	journal	February 2009
Spectral Networks and Fenchel–Nielsen Coordinates Hollands, Lotte; Neitzke, Andrew Letters in Mathematical Physics, Vol. 106, Issue 6 https://doi.org/10.1007/s11005-016-0842-x	journal	May 2016
Darboux coordinates, Yang-Yang functional, and gauge theory Nekrasov, N. A.; Rosly, A. A.; Shatashvili, S. L. Theoretical and Mathematical Physics, Vol. 181, Issue 1 https://doi.org/10.1007/s11232-014-0209-3	journal	October 2014
A remark on the scattering of BPS monopoles Manton, N. S. Physics Letters B, Vol. 110, Issue 1 https://doi.org/10.1016/0370-2693(82)90950-9	journal	March 1982
Self-dual strings and N = 2 supersymmetric field theory Klemm, Albrecht; Lerche, Wolfgang; Mayr, Peter Nuclear Physics B, Vol. 477, Issue 3 https://doi.org/10.1016/0550-3213(96)00353-7	journal	October 1996
Solutions of four-dimensional field theories via M-theory Witten, Edward Nuclear Physics B, Vol. 500, Issue 1-3 https://doi.org/10.1016/S0550-3213(97)00416-1	journal	September 1997
D-branes, monopoles and Nahm equations Diaconescu, Duiliu-Emanuel Nuclear Physics B, Vol. 503, Issue 1-2 https://doi.org/10.1016/S0550-3213(97)00438-0	journal	October 1997
Type IIB superstrings, BPS monopoles, and three-dimensional gauge dynamics Hanany, Amihay; Witten, Edward Nuclear Physics B, Vol. 492, Issue 1-2 https://doi.org/10.1016/S0550-3213(97)80030-2	journal	May 1997
Darboux coordinates, Yang-Yang functional, and gauge theory Nekrasov, N.; Rosly, A.; Shatashvili, S. Nuclear Physics B - Proceedings Supplements, Vol. 216, Issue 1 https://doi.org/10.1016/j.nuclphysbps.2011.04.150	journal	July 2011
Loop operators and S-duality from curves on Riemann surfaces Drukker, Nadav; Morrison, David R.; Okuda, Takuya Journal of High Energy Physics, Vol. 2009, Issue 09 https://doi.org/10.1088/1126-6708/2009/09/031	journal	September 2009
On the geometry and dynamics of diffeomorphisms of surfaces Thurston, William P. Bulletin of the American Mathematical Society, Vol. 19, Issue 2 https://doi.org/10.1090/S0273-0979-1988-15685-6	journal	April 1988
A note on the semiclassical formulation of BPS states in four-dimensional N=2 theories Brennan, T. Daniel; Moore, Gregory W. Progress of Theoretical and Experimental Physics, Vol. 2016, Issue 12 https://doi.org/10.1093/ptep/ptw159	journal	December 2016
Principal Moduli and Class Fields Cox, David; McKAY, John; Stevenhagen, Peter Bulletin of the London Mathematical Society, Vol. 36, Issue 01 https://doi.org/10.1112/S0024609303002583	journal	December 2003
The distribution of geodesic excursions into the neighborhood of a cone singularity on a hyperbolic 2-orbifold Haas, Andrew Commentarii Mathematici Helvetici, Vol. 83, Issue 1 https://doi.org/10.4171/cmh/115	journal	March 2008
Seiberg-Witten Prepotential from Instanton Counting Nekrasov, Nikita A. Advances in Theoretical and Mathematical Physics, Vol. 7, Issue 5 https://doi.org/10.4310/ATMP.2003.v7.n5.a4	journal	January 2003
Framed BPS states Gaiotto, Davide; Moore, Gregory W.; Neitzke, Andrew Advances in Theoretical and Mathematical Physics, Vol. 17, Issue 2 https://doi.org/10.4310/ATMP.2013.v17.n2.a1	journal	January 2013
Electric-magnetic duality and the geometric Langlands program Kapustin, Anton; Witten, Edward Communications in Number Theory and Physics, Vol. 1, Issue 1 https://doi.org/10.4310/CNTP.2007.v1.n1.a1	journal	January 2007
Loop operators and S-duality from curves on Riemann surfaces Drukker, Nadav; Morrison, David R.; Okuda, Takuya arXiv https://doi.org/10.48550/arxiv.0907.2593	text	January 2009
Framed BPS States Gaiotto, Davide; Moore, Gregory W.; Neitzke, Andrew arXiv https://doi.org/10.48550/arxiv.1006.0146	preprint	January 2010
Spectral networks Gaiotto, Davide; Moore, Gregory W.; Neitzke, Andrew arXiv https://doi.org/10.48550/arxiv.1204.4824	text	January 2012
On Monopole Bubbling Contributions to 't Hooft Loops Assel, Benjamin; Sciarappa, Antonio arXiv https://doi.org/10.48550/arxiv.1903.00376	text	January 2019
Electric-Magnetic Duality And The Geometric Langlands Program Kapustin, Anton; Witten, Edward arXiv https://doi.org/10.48550/arxiv.hep-th/0604151	preprint	January 2006
D-branes, Monopoles and Nahm Equations Diaconescu, Duiliu-Emanuel arXiv https://doi.org/10.48550/arxiv.hep-th/9608163	text	January 1996
Solutions Of Four-Dimensional Field Theories Via M Theory Witten, Edward arXiv https://doi.org/10.48550/arxiv.hep-th/9703166	text	January 1997
D-particle bound states and generalized instantons Moore, G.; Nekrasov, N.; Shatashvili, S. arXiv https://doi.org/10.48550/arxiv.hep-th/9803265	text	January 1998
Principal moduli and class fields Cox, David; McKay, John; Stevenhagen, Peter arXiv https://doi.org/10.48550/arxiv.math/0311202	preprint	January 2003

Cited By (2)

’t Hooft defects and wall crossing in SQM Brennan, T. Daniel; Dey, Anindya; Moore, Gregory W. Journal of High Energy Physics, Vol. 2019, Issue 10 https://doi.org/10.1007/jhep10(2019)173	journal	October 2019
't Hooft Defects and Wall Crossing in SQM Brennan, T. Daniel; Dey, Anindya; Moore, Gregory W. arXiv https://doi.org/10.48550/arxiv.1810.07191	text	January 2018

Similar Records

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

Journal Article · 2018 · Journal of High Energy Physics (Online) · OSTI ID:1502391

Brennan, T. Daniel; Dey, Anindya; Moore, Gregory W.

Exact WKB and the quantum Seiberg-Witten curve for 4d $N$ = 2 pure SU(3) Yang-Mills. Abelianization

Journal Article · 2022 · Journal of High Energy Physics (Online) · OSTI ID:1976461

Yan, Fei

Monopole bubbling via string theory

Journal Article · 2018 · Journal of High Energy Physics (Online) · OSTI ID:1611321

Brennan, T. Daniel

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
Differential and Algebraic Geometry
Physics
Supersymmetric Gauge Theory
Wilson
’t Hooft and Polyakov loops

Title: Index-like theorems from line defect vevs

Citation Formats

References (48)

Cited By (2)

Similar Records

Related Subjects