3d Deconfinement, Product gauge group, Seiberg-Witten and New 3d dualities
We construct a three dimensional deconfinement method which enables us to find new three-dimensional dualities and we apply various techniques developed in four dimensional supersymmetric gauge theories, such as the product gauge groups and Seiberg-Witten curves to the three dimensional $\mathcal{N}=2$ supersymmetric gauge theories. Dual descriptions of three dimensional $\mathcal{N}=2$ supersymmetric gauge theories which involve two-index matters, for example, adjoint, symmetric, and anti-symmetric matters without superpotentials can be obtained. These matters are described in terms of s-confining phases of the supersymmetric gauge theories.