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Partition function of N = 2* SYM on a large four-sphere

Timothy Hollowood Orcid Logo, Prem Kumar Orcid Logo

Journal of High Energy Physics, Volume: 2015, Issue: 12

Swansea University Authors: Timothy Hollowood Orcid Logo, Prem Kumar Orcid Logo

DOI (Published version): 10.1007/JHEP12(2015)016

Abstract

We examine the partition function of N=2* supersymmetric SU(N) Yang-Mills theory on the four-sphere in the large radius limit. We point out that the large radius partition function, at fixed N, is computed by saddle points lying on particular walls of marginal stability on the Coulomb branch of the...

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Published in: Journal of High Energy Physics
Published: 2015
Online Access: https://inspirehep.net/record/1391534/files/scoap3-fulltext.pdf?subformat=pdfa
URI: https://cronfa.swan.ac.uk/Record/cronfa23373
first_indexed 2015-09-21T02:08:55Z
last_indexed 2020-07-16T12:39:46Z
id cronfa23373
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spelling 2020-07-16T12:31:47.4517674 v2 23373 2015-09-20 Partition function of N = 2* SYM on a large four-sphere ea9ca59fc948276ff2ab547e91bdf0c2 0000-0002-3258-320X Timothy Hollowood Timothy Hollowood true false 087fd097167d724ce1b13cb285741ef5 0000-0003-0867-4213 Prem Kumar Prem Kumar true false 2015-09-20 BGPS We examine the partition function of N=2* supersymmetric SU(N) Yang-Mills theory on the four-sphere in the large radius limit. We point out that the large radius partition function, at fixed N, is computed by saddle points lying on particular walls of marginal stability on the Coulomb branch of the theory on R^4. For N an even (odd) integer and \theta_YM=0, (\pi), these include a point of maximal degeneration of the Donagi-Witten curve to a torus where BPS dyons with electric charge [N/2] become massless. We argue that the dyon singularity is the lone saddle point in the SU(2) theory, while for SU(N) with N>2, we characterize potentially competing saddle points by obtaining the relations between the Seiberg-Witten periods at such points. Using Nekrasov's instanton partition function, we solve for the maximally degenerate saddle point and obtain its free energy as a function of g_YM and N, and show that the results are "large-N exact". In the large-N theory our results provide analytical expressions for the periods/eigenvalues at the maximally degenerate saddle point, precisely matching previously known formulae following from the correspondence between N=2* theory and the elliptic Calogero-Moser integrable model. The maximally singular point ceases to be a saddle point of the partition function above a critical value of the coupling, in agreement with the recent findings of Russo and Zarembo. Journal Article Journal of High Energy Physics 2015 12 Supersymmetric gauge theory, localisation, Seiberg-Witten theory 31 12 2015 2015-12-31 10.1007/JHEP12(2015)016 https://inspirehep.net/record/1391534/files/scoap3-fulltext.pdf?subformat=pdfa COLLEGE NANME Biosciences Geography and Physics School COLLEGE CODE BGPS Swansea University 2020-07-16T12:31:47.4517674 2015-09-20T20:44:02.6367666 Faculty of Science and Engineering School of Biosciences, Geography and Physics - Physics Timothy Hollowood 0000-0002-3258-320X 1 Prem Kumar 0000-0003-0867-4213 2 0023373-07122015185927.pdf scoap3-fulltext.pdf 2015-12-07T18:59:27.7730000 Output 791043 application/pdf Accepted Manuscript true 2015-12-07T00:00:00.0000000 false
title Partition function of N = 2* SYM on a large four-sphere
spellingShingle Partition function of N = 2* SYM on a large four-sphere
Timothy Hollowood
Prem Kumar
title_short Partition function of N = 2* SYM on a large four-sphere
title_full Partition function of N = 2* SYM on a large four-sphere
title_fullStr Partition function of N = 2* SYM on a large four-sphere
title_full_unstemmed Partition function of N = 2* SYM on a large four-sphere
title_sort Partition function of N = 2* SYM on a large four-sphere
author_id_str_mv ea9ca59fc948276ff2ab547e91bdf0c2
087fd097167d724ce1b13cb285741ef5
author_id_fullname_str_mv ea9ca59fc948276ff2ab547e91bdf0c2_***_Timothy Hollowood
087fd097167d724ce1b13cb285741ef5_***_Prem Kumar
author Timothy Hollowood
Prem Kumar
author2 Timothy Hollowood
Prem Kumar
format Journal article
container_title Journal of High Energy Physics
container_volume 2015
container_issue 12
publishDate 2015
institution Swansea University
doi_str_mv 10.1007/JHEP12(2015)016
college_str Faculty of Science and Engineering
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hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Biosciences, Geography and Physics - Physics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Biosciences, Geography and Physics - Physics
url https://inspirehep.net/record/1391534/files/scoap3-fulltext.pdf?subformat=pdfa
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description We examine the partition function of N=2* supersymmetric SU(N) Yang-Mills theory on the four-sphere in the large radius limit. We point out that the large radius partition function, at fixed N, is computed by saddle points lying on particular walls of marginal stability on the Coulomb branch of the theory on R^4. For N an even (odd) integer and \theta_YM=0, (\pi), these include a point of maximal degeneration of the Donagi-Witten curve to a torus where BPS dyons with electric charge [N/2] become massless. We argue that the dyon singularity is the lone saddle point in the SU(2) theory, while for SU(N) with N>2, we characterize potentially competing saddle points by obtaining the relations between the Seiberg-Witten periods at such points. Using Nekrasov's instanton partition function, we solve for the maximally degenerate saddle point and obtain its free energy as a function of g_YM and N, and show that the results are "large-N exact". In the large-N theory our results provide analytical expressions for the periods/eigenvalues at the maximally degenerate saddle point, precisely matching previously known formulae following from the correspondence between N=2* theory and the elliptic Calogero-Moser integrable model. The maximally singular point ceases to be a saddle point of the partition function above a critical value of the coupling, in agreement with the recent findings of Russo and Zarembo.
published_date 2015-12-31T00:59:16Z
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