Effect of topological excitations in the two-dimensional quantum Heisenberg antiferromagnet

Using a continuum large-N U(1) gauge theory (${\mathrm{CP}}^{\mathit{N}\mathrm{-}1}$) for the low-temperature antiferromagnet in 2+1 dimensions, we recover previously obtained results for the static correlation length at the mean-field level. Phase fluctuations about mean field result in soundlike collective modes among a topological domain-wall loop liquid. To order ${\mathit{N}}^{\mathrm{-}1}$, the sound modes are gapless in the quantum disordered phase. In the Néel phase they have small gaps, which results in an anomalous contribution to the spin-wave damping near the antiferromagnetic Bragg point.