Higgs branches of U/SU quivers via brane locking

We solve a long standing problem on the computation of the Higgs branch $$ \mathcal{H} $$ of linear quivers with 8 supercharges and with both unitary and special unitary gauge nodes. The solution uses the concept of magnetic quivers, where components of $$ \mathcal{H} $$ are described as 3d $$ \mathcal{N} $$ = 4 Coulomb branches. When the starting quiver is good, there is a single component in $$ \mathcal{H} $$ and the magnetic quiver is a 3d mirror. The magnetic quivers are obtained from studying the brane web for an auxiliary 5d theory (with only special unitary gauge groups), constrained by a new notion called brane locking, where some branes are required to move together. We view this as a computational tool rather than an operation in 5d. A detailed algorithm is provided.