Electron spin resonance in high-field critical phase of gapped spin chains

Motivated by recent experiments on $\mathrm{Ni}({\mathrm{C}}_{2}{\mathrm{H}}_{8}{\mathrm{N}}_{2}{)}_{2}\mathrm{Ni}(\mathrm{CN}{)}_{4}$ (commonly known as NENC), we study the electron spin resonance in the critical high-field phase of the antiferromagnetic $S=1$ chain with strong planar anisotropy and show that the ESR spectra exhibit several peculiarities in the critical phase. Possible relevance of those results for other gapped spin systems is discussed.