  First, we briefly review the solar abundance problem and its current status.
We start with the description of the existing theoretical model of the Sun and
its main uncertainties and proceed with the discussion of the observational
evidence for the anomaly. We conclude the review part by outlining the main
approaches to solving the solar abundance problem investigated before. In the
second part of the paper we consider the poorly studied before non-diffusive
energy transport solutions to the problem. We calculate the additional energy
flux inside the Sun evidenced by the combined data from helioseismology,
spectroscopy and solar neutrino detection experiments. Our findings suggest
that the solar abundance problem can be solved by a localized loss of energy
near the radiative zone boundary and a gain of approximately the same amount of
energy inside the solar core ($0.1R_{\odot} \lesssim r \lesssim 0.3R_{\odot}$).
We show that if the localized loss of energy is associated with the resonant
emission of transversely polarized hidden photons, the kinetic mixing parameter
required does not contradict any of the existing constraints, the ones from the
Sun being relaxed as long as the energy loss is compensated by energy
deposition inside the core. We introduce then the light dark fermions coupled
to hidden photons and discuss their interactions with the solar plasma. We find
the distribution of these dark particles inside the inner part of the radiative
zone which is required to provide the necessary heating of the core.
