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We consider mixed branches of 3d $mathcal{N}=4$ $T[SU(N)]$ theory. We compute the Hilbert series of the Coulomb branch part of the mixed branch from a restriction rule acting on the Hilbert series of the full Coulomb branch that will truncate the magnetic charge summation only to the subset of BPS dressed monopole operators that arise in the Coulomb branch sublocus where the mixed branch stems. This restriction can be understood directly from the type IIB brane picture by a relation between the magnetic charges of the monopoles and brane position moduli. We also apply the restriction rule to the Higgs branch part of a given mixed branch by exploiting 3d mirror symmetry. Both cases show complete agreement with the results calculated by different methods.
We study the domain walls in hot $4$-D $SU(N)$ super Yang-Mills theory and QCD(adj), with $n_f$ Weyl flavors. We find that the $k$-wall worldvolume theory is $2$-D QCD with gauge group $SU(N-k)times SU(k) times U(1)$ and Dirac fermions charged under
We consider a semi-classical treatment, in the regime of weak gauge coupling, of supersymmetric Yang-Mills theory in a space-time of the form T^3xR with SU(n)/Z_n gauge group and a non-trivial gauge bundle. More specifically, we consider the theories
Color confinement is the most puzzling phenomenon in the theory of strong interaction based on a quantum SU(3) Yang-Mills theory. The origin of color confinement supposed to be intimately related to non-perturbative features of the non-Abelian gauge
We describe how simple machine learning methods successfully predict geometric properties from Hilbert series (HS). Regressors predict embedding weights in projective space to ${sim}1$ mean absolute error, whilst classifiers predict dimension and Gor
We study $mathcal{N} = 3$ supersymmetric Chern-Simons-matter theory coupled to matter in the fundamental representation of $SU(N)$. In the t Hooft large $N$ limit, we compute the exact $2 to 2$ scattering amplitudes of the fundamental scalar superfie