Abstract
We study the (m)-type connected correlation functions of OPE blocks with respect to one spatial region in two dimensional conformal field theory. We find a logarithmic divergence for these correlation functions. We justify the logarithmic behaviour from two different approaches: massless free scalar theory and conformal block. Cutoff independent coefficients are obtained from analytic continuation of conformal blocks. A UV/IR relation has been found in the connected correlation functions. We could derive a formal “first law of thermodynamics” for a subsystem using the deformed reduced density matrix. An area law of the connected correlation function in higher dimensions is also discussed briefly.
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