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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 andits main uncertainties and proceed with the discussion of the observationalevidence for the anomaly. We conclude the review part by outlining the mainapproaches to solving the solar abundance problem investigated before. In thesecond part of the paper we consider the poorly studied before non-diffusiveenergy transport solutions to the problem. We calculate the additional energyflux inside the Sun evidenced by the combined data from helioseismology,spectroscopy and solar neutrino detection experiments. Our findings suggestthat the solar abundance problem can be solved by a localized loss of energynear the radiative zone boundary and a gain of approximately the same amount ofenergy 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 resonantemission of transversely polarized hidden photons, the kinetic mixing parameterrequired does not contradict any of the existing constraints, the ones from theSun being relaxed as long as the energy loss is compensated by energydeposition inside the core. We introduce then the light dark fermions coupledto hidden photons and discuss their interactions with the solar plasma. We findthe distribution of these dark particles inside the inner part of the radiativezone which is required to provide the necessary heating of the core.

Generic energy transport solutions to the solar abundance problem -- a hint of new physics