Correlation functions in the holographic replica method

Disorder has long been a difficult subject in condensed matter systems and the The replica method is a well-known tool in this field. Implementing the replica method the AdS/CFT correspondence has been proposed and discussed in literatures. We point out, for any CFT that has a holographic dual and to the leading order of the large-N expansion, the corrections due to the presence of random disorder to any connected correlation functions vanish identically, provided that the disorder strength is normalized as discussed in literatures and that the symmetry among replicas is unbroken. Same must hold true to any observables that are determined by the connected correlation functions through a linear relation. This behavior resembles strongly that of a free theory where disorder is coupled to the fundamental field. We demonstrate this by both the means of holographic principle and field theory analysis in a toy model. We also propose ways of evaluating the non-zero sub-leading effects perturbatively in terms of the disorder strength and discuss a novel possibility of defining a new holographic dual if we adopt a different normalization for the disorder strength.