A construction of quarter BPS coherent states and Brauer algebras

TL;DR

This paper constructs quarter BPS coherent states using matrix fields and Brauer algebra representations, providing new tools for understanding their structure and overlaps, with implications for semiclassical geometries in gauge/gravity duality.

Contribution

It introduces a novel construction of quarter BPS coherent states based on Brauer algebra representations, extending the understanding beyond half BPS states.

Findings

Constructed quarter BPS coherent states with matrix fields.

Derived overlaps between Brauer states and coherent states.

Computed entanglement entropy and overlaps with squeezed states.

Abstract

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.