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Nilpotent orbits and the Coulomb branch of T σ | ( G | ) theories: special orthogonal vs orthogonal gauge group factors

Coulomb branches of a set of 3 d N$$ \mathcal{N} $$= 4 supersymmetric gauge theories are closures of nilpotent orbits of the algebra so n$$ \mathfrak{so}(n) $$. From the point of view of string theory, these quantum field theories can be understood as effective gauge theories describing the low ener... Full description

Main Author: Cabrera, Santiago
Contributors: Hanany, Amihay | Author
Zhong, Zhenghao | Author
Contained in: Journal of High Energy Physics Berlin : Springer Vol. 2017, No. 11 (2017), p. 1-29
Journal Title: Journal of High Energy Physics
Fulltext access: Fulltext access (direct link - free access) 10.1007/JHEP11(2017)079
Availability is being checked...
Links: Volltext (dx.doi.org)
ISSN: 1029-8479
Additional Keywords: Brane Dynamics in Gauge Theories
Field Theories in Lower Dimensions
Gauge Symmetry
OriginalPaper
Supersymmetric Gauge Theory
DOI: 10.1007/JHEP11(2017)079
Language: English
Notes: Open Access
A r X iv e P rint:1707.06941
Physical Description: Online-Ressource
ID (e.g. DOI, URN): 10.1007/JHEP11(2017)079
JHEP11(2017)079
PPN (Catalogue-ID): SPR060297271
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520 |a Coulomb branches of a set of 3 d N$$ \mathcal{N} $$= 4 supersymmetric gauge theories are closures of nilpotent orbits of the algebra so n$$ \mathfrak{so}(n) $$. From the point of view of string theory, these quantum field theories can be understood as effective gauge theories describing the low energy dynamics of a brane configuration with the presence of orientifold planes [1]. The presence of the orientifold planes raises the question to whether the orthogonal factors of a the gauge group are indeed orthogonal O( N) or special orthogonal SO( N). In order to investigate this problem, we compute the Hilbert series for the Coulomb branch of Tσ(SO( n)∨) theories, utilizing the monopole formula. The results for all nilpotent orbits from so3$$ \mathfrak{so}(3) $$ to so10$$ \mathfrak{so}(10) $$ which are special and normal are presented. A new relationship between the choice of SO/O( N) factors in the gauge group and the Lusztig’s Canonical Quotient A¯ Oλ$$ \overline{A}\left({\mathcal{O}}_{\lambda}\right) $$ of the corresponding nilpotent orbit is observed. We also provide a new way of projecting several magnetic lattices of different SO( N) gauge group factors by the diagonal action of aℤ2$$ {\mathbb{Z}}_2 $$ group. 
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653 |a Supersymmetric Gauge Theory 
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700 1 |a Zhong, Zhenghao  |e verfasserin  |4 aut 
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