Entanglement Renyi entropies in conformal field theories and holography

An entanglement Renyi entropy for a spatial partition of a system is studied in conformal theories which admit a dual description in terms of an anti-de Sitter gravity. The divergent part of the Renyi entropy is computed in 4D conformal N = 4 super Yang-Mills theory at a weak coupling. This result is used to suggest a holographic formula which reproduces the Renyi entropy at least in the leading approximation. The holographic Renyi entropy is an invariant functional set on a codimension 2 minimal hypersurface in the bulk geometry. The bulk space does not depend on order n of the Renyi entropy. The holographic Renyi entropy is a sum of local and non-local functionals multiplied by polynomials of 1/n.