Ring Relations and Mirror Map from Branes

Understand

We study the space of vacua of three-dimensional $\mathcal{N}=4$ theories from a novel approach building on the type IIB brane realization of the theory and in which the insertion of local chiral operators in the path integral is obtained from integrating out light modes in appropriate brane setups.

• Most of our analysis focuses on abelian quiver theories which can be realized as the low-energy theory of D3-D5-NS5 brane arrays.
• Their space of vacua contains a Higgs branch, parametrized by the vevs of half-BPS meson operators, and a Coulomb branch, parametrized by the vevs of half-BPS monopole operators.
• We show that the Higgs operators are inserted by adding F1 strings and D3 branes, while the Coulomb operators are inserted by adding D1 strings and D3 branes, with specific orientations, to the initial brane setup of the theory.