This thesis contains research conducted on various topics in quantum field theory and string theory. The first two chapters study certain aspects of gauge/gravity duality. In particular, the first considers gravity duals to a metastable supersymmetry breaking vacua while the second studies duals to certain anisotropic critical points. The third chapter shows the existence of a universal term in the entanglement entropy for a certain class of fixed points via a quantum field theoretic perspective. The fourth chapter studies how the boundary entropy of a two-dimensional conformal field theory changes when the bulk theory is perturbed by a relevant operator. |