The instrumental advances made in this new era of 4 m class solar telescopes with unmatched spectropolarimetric accuracy and sensitivity will enable the study of chromospheric magnetic fields and their dynamics with unprecedented detail. In this regard, spectropolarimetric diagnostics can provide invaluable insight into magneto-hydrodynamic (MHD) wave processes. MHD waves and, in particular, Alfvénic fluctuations associated with particular wave modes were recently recognized as important mechanisms not only for the heating of the outer layers of the Sun’s atmosphere and the acceleration of the solar wind, but also for the elemental abundance anomaly observed in the corona of the Sun and other Sun-like stars (also known as first ionization potential) effect. Here, we take advantage of state-of-the-art and unique spectropolarimetric Interferometric BIdimensional Spectrometer observations to investigate the relation between intensity and circular polarization (CP) fluctuations in a sunspot chromosphere. Our results show a clear link between the intensity and CP fluctuations in a patch which corresponds to a narrow range of magnetic field inclinations. This suggests the presence of Alfvénic perturbations in the sunspot. This article is part of the Theo Murphy meeting issue ‘High-resolution wave dynamics in the lower solar atmosphere’.