Advances in Theoretical and Mathematical Physics

Volume 24 (2020)

Number 5

A construction of quarter BPS coherent states and Brauer algebras

Pages: 1111 – 1169

DOI: https://dx.doi.org/10.4310/ATMP.2020.v24.n5.a3

Authors

Hai Lin (Yau Mathematical Sciences Center and Department of Mathematical Sciences, Tsinghua University, Beijing, China)

Keyou Zeng (Department of Physics, Tsinghua University, Beijing, China; and Perimeter Institute for Theoretical Physics, Waterloo, Ontario, Canada)

Abstract

BPS coherent states 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 the annihilation operators and in the kernel of the anomalous dimension 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 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 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.

Published 7 July 2021