On Higgs branch localization of Seiberg–Witten theories on an ellipsoid

In this note, we consider so-called “Higgs branch localization” for four-dimensional ${\mathcal {N}}=2$ field theories on a 4D ellipsoid. We find a new set of saddle point equations arising from the additional Higgs branch deformation term, whose solutions include both Higgs branch and BPS instanton...

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Bibliographic Details
Published inProgress of theoretical and experimental physics Vol. 2016; no. 1; p. 13
Main Authors Chen, Heng-Yu, Tsai, Tsung-Hsuan
Format Journal Article
LanguageEnglish
Published Oxford University Press 01.01.2016
Subjects
B10
B00
B35
B16
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Summary:In this note, we consider so-called “Higgs branch localization” for four-dimensional ${\mathcal {N}}=2$ field theories on a 4D ellipsoid. We find a new set of saddle point equations arising from the additional Higgs branch deformation term, whose solutions include both Higgs branch and BPS instanton–vortex mixed configurations. By evaluating the contour integral, we also demonstrate that the ellipsoid partition almost factorizes into purely $b$ - and $b^{-1}$ -dependent parts, using SQCD as an explicit example. We identify various factorized parts with the ellipsoid partition function of two-dimensional ${\mathcal {N}}=(2,2)$ SQCDA, which is precisely the vortex world volume theory. We also give a physical interpretation for the non-factorizable parts and discuss future directions.
ISSN:2050-3911
2050-3911
DOI:10.1093/ptep/ptv188