  It remains unclear which physical processes are responsible for the dramatic
increase with height of the temperature in stellar atmospheres, known as the
chromospheric ($\sim$10,000 K) and coronal (several million K) heating
problems. Statistical studies of sun-like stars reveal that chromospheric and
coronal emissions are correlated on a global scale, constraining, in principle,
theoretical models of potential heating mechanisms. However, so far, spatially
resolved observations of the Sun have surprisingly failed to show a similar
correlation on small spatial scales, leaving models poorly constrained. Here we
use unique coordinated high-resolution observations of the chromosphere (from
the Interface Region Imaging Spectrograph or IRIS satellite) and low corona
(from the Hi-C 2.1 sounding rocket), and machine-learning based inversion
techniques to show a strong correlation on spatial scales of a few hundred km
between heating in the chromosphere and low corona for regions with strong
magnetic field ("plage"). These results are compatible with recent advanced 3D
radiative magnetohydrodynamic simulations in which dissipation of current
sheets formed due to the braiding of the magnetic field lines deep in the
atmosphere is responsible for heating the plasma simultaneously to
chromospheric and coronal temperatures. Our results provide deep insight into
the nature of the heating mechanism in solar active regions.
