Folding orthosymplectic quivers

Abstract

Folding identical legs of a simply-laced quiver creates a quiver with a non-simply laced edge. So far, this has been explored for quivers containing unitary gauge groups. In this paper, orthosymplectic quivers are folded, giving rise to a new family of quivers. This is realised by intersecting orientifolds in the brane system. The monopole formula for these non-simply laced orthosymplectic quivers is introduced. Some of the folded quivers have Coulomb branches that are closures of minimal nilpotent orbits of exceptional algebras, thus providing a new construction of these fundamental moduli spaces. Moreover, a general family of folded orthosymplectic quivers is shown to be a new magnetic quiver realisation of Higgs branches of 4d $$ \mathcal{N} $$ N = 2 theories. The Hasse (phase) diagrams of certain families are derived via quiver subtraction as well as Kraft-Procesi transitions in the brane system.

Magnetic quivers and line defects — On a duality between 3d $$ \mathcal{N} $$ = 4 unitary and orthosymplectic quivers

“…It is then a choice to remove this discrete group from the gauge group or not, as both choices lead to well-defined theories. However, in view of the unframed orthosymplectic magnetic quivers studied in [5,6,9,15,16,25,27], the choice of removing the diagonal Z 2 seems preferred from brane configurations. To be specific, consider the example SO(2n) Sp(k) (2.19) such that G = SO(2n) × Sp(k).…”

“…These changes are due to new massless degrees of freedom arising from tensionless strings in 6d, massless gauge instantons in 5d, and Argyres-Douglas points in 4d. Recently, magnetic quivers [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] have been systematically introduced with the aim to uniformly address Higgs branches of theories with 8 supercharges in dimensions 4 to 6. For this an auxiliary quiver gauge theory Q is utilised such that its 3d N = 4 Coulomb branch C provides a geometric description of the desired Higgs branch H of a theory T in a phase P : H (T, P ) = C (Q(T, P )) .…”

Balanced B and D-type orthosymplectic quivers -- Magnetic quivers for product theories

“…• C-type orthosymplectic quivers, most notably those obtained by folding A-type quivers, have been explored recently in [11].…”

“…In particular, these include quivers without flavour nodes -hereafter referred as unframed quivers. These developments are largely based on an improved understanding of generating functions, like the Coulomb branch Hilbert series [1,10,11]. This greatly expands the set of orthosymplectic quivers one can probe and the time is ripe for a systematic exploration.…”

Magnetic quivers and line defects -- On a duality between 3d N=4 unitary and orthosymplectic quivers

“…These changes are due to new massless degrees of freedom arising from tensionless strings in 6d, massless gauge instantons in 5d, and Argyres-Douglas points in 4d. Recently, magnetic quivers [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] have been systematically introduced with the aim to uniformly address Higgs branches of theories with 8 supercharges in dimensions 4 to 6. For this an auxiliary quiver gauge theory Q is utilised such that its 3d N = 4 Coulomb branch C provides a geometric description of the desired Higgs branch H of a theory T in a phase P : H (T, P ) = C (Q(T, P )) .…”