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Quantization of integrable systems and a 2d/4d duality

Nick Dorey, Sungjay Lee, Timothy Hollowood Orcid Logo

Journal of High Energy Physics, Volume: 2011, Issue: 10, Start page: 077

Swansea University Author: Timothy Hollowood Orcid Logo

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DOI (Published version): 10.1007/JHEP10(2011)077

Abstract

We present a new duality between the F-terms of supersymmetric field theories defined in two- and four-dimensions respectively. The duality relates N=2 supersymmetric gauge theories in four dimensions, deformed by an Omega-background in one plane, to N=(2,2) gauged linear sigma-models in two dimensi...

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Published in: Journal of High Energy Physics
ISSN: 1029-8479
Published: Springer 2011
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URI: https://cronfa.swan.ac.uk/Record/cronfa7245
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spelling 2015-07-10T13:30:45.4232837 v2 7245 2012-02-23 Quantization of integrable systems and a 2d/4d duality ea9ca59fc948276ff2ab547e91bdf0c2 0000-0002-3258-320X Timothy Hollowood Timothy Hollowood true false 2012-02-23 SPH We present a new duality between the F-terms of supersymmetric field theories defined in two- and four-dimensions respectively. The duality relates N=2 supersymmetric gauge theories in four dimensions, deformed by an Omega-background in one plane, to N=(2,2) gauged linear sigma-models in two dimensions. On the four dimensional side, our main example is N=2 SQCD with gauge group SU(L) and 2L fundamental flavours. Using ideas of Nekrasov and Shatashvili, we argue that the Coulomb branch of this theory provides a quantization of the classical Heisenberg SL(2) spin chain. Agreement with the standard quantization via the Algebraic Bethe Ansatz implies the existence of an isomorphism between the chiral ring of the 4d theory and that of a certain two-dimensional theory. The latter can be understood as the worldvolume theory on a surface operator/vortex string probing the Higgs branch of the same 4d theory. We check the proposed duality by explicit calculation at low orders in the instanton expansion. One striking consequence is that the Seiberg-Witten solution of the 4d theory is captured by a one-loop computation in two dimensions. The duality also has interesting connections with the AGT conjecture, matrix models and topological string theory where it corresponds to a refined version of the geometric transition. Journal Article Journal of High Energy Physics 2011 10 077 Springer 1029-8479 31 12 2011 2011-12-31 10.1007/JHEP10(2011)077 COLLEGE NANME Physics COLLEGE CODE SPH Swansea University 2015-07-10T13:30:45.4232837 2012-02-23T17:01:49.0000000 Faculty of Science and Engineering School of Biosciences, Geography and Physics - Physics Nick Dorey 1 Sungjay Lee 2 Timothy Hollowood 0000-0002-3258-320X 3
title Quantization of integrable systems and a 2d/4d duality
spellingShingle Quantization of integrable systems and a 2d/4d duality
Timothy Hollowood
title_short Quantization of integrable systems and a 2d/4d duality
title_full Quantization of integrable systems and a 2d/4d duality
title_fullStr Quantization of integrable systems and a 2d/4d duality
title_full_unstemmed Quantization of integrable systems and a 2d/4d duality
title_sort Quantization of integrable systems and a 2d/4d duality
author_id_str_mv ea9ca59fc948276ff2ab547e91bdf0c2
author_id_fullname_str_mv ea9ca59fc948276ff2ab547e91bdf0c2_***_Timothy Hollowood
author Timothy Hollowood
author2 Nick Dorey
Sungjay Lee
Timothy Hollowood
format Journal article
container_title Journal of High Energy Physics
container_volume 2011
container_issue 10
container_start_page 077
publishDate 2011
institution Swansea University
issn 1029-8479
doi_str_mv 10.1007/JHEP10(2011)077
publisher Springer
college_str Faculty of Science and Engineering
hierarchytype
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
document_store_str 0
active_str 0
description We present a new duality between the F-terms of supersymmetric field theories defined in two- and four-dimensions respectively. The duality relates N=2 supersymmetric gauge theories in four dimensions, deformed by an Omega-background in one plane, to N=(2,2) gauged linear sigma-models in two dimensions. On the four dimensional side, our main example is N=2 SQCD with gauge group SU(L) and 2L fundamental flavours. Using ideas of Nekrasov and Shatashvili, we argue that the Coulomb branch of this theory provides a quantization of the classical Heisenberg SL(2) spin chain. Agreement with the standard quantization via the Algebraic Bethe Ansatz implies the existence of an isomorphism between the chiral ring of the 4d theory and that of a certain two-dimensional theory. The latter can be understood as the worldvolume theory on a surface operator/vortex string probing the Higgs branch of the same 4d theory. We check the proposed duality by explicit calculation at low orders in the instanton expansion. One striking consequence is that the Seiberg-Witten solution of the 4d theory is captured by a one-loop computation in two dimensions. The duality also has interesting connections with the AGT conjecture, matrix models and topological string theory where it corresponds to a refined version of the geometric transition.
published_date 2011-12-31T03:09:00Z
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score 11.013148

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