It is a classical inequality that the minimum of the ratio of the (weighted) arithmetic mean to the geometric mean of a set of positive variables is equal to one, and is attained at the center of the positivity cone. While there are numerous proofs of this fundamental homogeneous inequality, in the presence of an arbitrary subspace, and/or the replacement of the arithmetic mean with an arbitrar...

We study 3d $\mathcal{N}=2$ SQCD with symplectic and orthogonal gauge groups adjoint matter. For $USp(2n)$ two fundamentals $SO(N)$ one vector these models have been recently shown to s-confine. Here we corroborate the validity of this proposal by relating it confinement four an antisymmetric tensor, using exact mathematical results coming from analysis partition function on squashed three-sphe...

A bstract We present various 4d $$ \mathcal{N} N = 1 theories enjoying IR global symmetry enhancement. The models we consider have the USp(2 N ) gauge group, 8 fundamental, one antisymmetric chirals and numbers of singlets. By suitably turning on superpotential deformations involving singlets which break part...