Two new mechanisms of light absorption by a fractal cluster are considered. Both mechanisms are born out by specific features of the photon trajectory topology in the system of correlated scatterers. This trajectory, under certain circumstances, can become null-dimensional Antuan's set, the so-called Antuan's necklace. The first absorption mechanism results from the topological prohibition for the Antuan's null-dimensional photon to escape to space with a traditional topological dimensionality d = 1,2,3. The second mechanism relies upon a sort of "mechanical" rigidity of the Antuan's trajectory. This rigidity is related to the singularity of Antuan's photon energy density resulting from the transformation of an actual three-dimensional photon to a null-dimensional object. Photon cannot leave a cluster because of the difficulties with breaking up the necklaced virtual Antuan's chains. Absorption cross sections for fractal clusters are calculated for both mechanisms.