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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: 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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 LEADER 001 02538nma a2200373 c 4500 SPR060297271 DE-601 20171116204555.0 cr uuu---uuuuu 171116s2017 000 0 eng d 7 |a 10.1007/JHEP11(2017)079  |2 doi 8 |a JHEP11(2017)079 |a JHEP11(2017)079 |b ger  |c GBVCP 0 |a eng 1 |a Cabrera, Santiago 1 0 |a Nilpotent orbits and the Coulomb branch of T σ | ( G | ) theories: special orthogonal vs orthogonal gauge group factors  |h Elektronische Ressource |a Online-Ressource |a Open Access |a A r X iv e P rint:1707.06941 |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. |a OriginalPaper |a Field Theories in Lower Dimensions |a Gauge Symmetry |a Supersymmetric Gauge Theory |a Brane Dynamics in Gauge Theories 1 |a Hanany, Amihay  |e verfasserin  |4 aut 1 |a Zhong, Zhenghao  |e verfasserin  |4 aut 0 8 |i in  |t Journal of High Energy Physics  |d Berlin : Springer  |g Vol. 2017, No. 11 (2017), p. 1-29  |q 2017:11<1-29  |w (DE-601)SPR047830530  |x 1029-8479 4 1 |u http://dx.doi.org/10.1007/JHEP11(2017)079  |z OA  |3 Volltext |a GBV_SPRINGER |a OPENACCESS |a AR |d 2017  |j 2017  |e 11  |c 11  |h 1-29