  BPS coherent states closely resemble semiclassical states and they have
gravity dual descriptions in terms of semiclassical geometries. The half BPS
coherent states have been well studied, however less is known about quarter BPS
coherent states. Here we provide a construction of quarter BPS coherent states.
They are coherent states built with two matrix fields, generalizing the half
BPS case. These states are both the eigenstates of annihilation operators and
in the kernel of dilatation operator. Another useful labeling of quarter BPS
states is by representations of Brauer algebras and their projection onto a
subalgebra $\mathbb{C}[S_n\times S_m]$. Here, the Schur-Weyl duality for the
Walled Brauer algebra plays an important role in organizing the operators. One
interesting subclass of these Brauer states are labeled by representations
involving two Young tableaux. We obtain the overlap between quarter BPS Brauer
states and quarter BPS coherent states, where the Schur polynomials are used.
We also derive superposition formulas transforming a truncated version of
quarter BPS coherent states to quarter BPS Brauer states. The entanglement
entropy of Brauer states as well as the overlap between Brauer states and
squeezed states are also computed.
