Holographic entanglement entropy, subregion complexity and some related topics are introduced at the beginning of this thesis . Then we study different families of singular subregions in the dual field theory and find the divergence structure and universal terms of holographic subregion complexity for these singular surfaces . We find that there is new universal terms , logarithmic in the UV cut-off , due to the singularities for a family of surfaces including a kink in (2+1)-dimension and cones in even dimensional field theories . We also find examples of new divergent structures such as quadratic in logarithm of the UV cut-off and also negative powers of the UV cut-off times its logarithm . Our results show new divergence terms in comparison with smooth subregions for some singular surfaces with flat locus . In the framework of the AdS/CFT correspondence , imposing a scalar field in the bulk space-time leads to deform the corresponding CFT in the boundary , which may produce corrections to entanglement entropy , as well as the so-called subregion complexity . We have computed such corrections for a set of singular subregions including kink , cones and creases in different dimensions . Our calculations shows new singular terms including universal logarithmic corrections for entanglement entropy and subregion complexity for some distinct values of conformal weight .
