  We study a proper definition of R\'enyi mutual information (RMI) in quantum
field theory as defined via the Petz R\'enyi relative entropy. Unlike the
standard definition, the RMI we compute is a genuine measure of correlations
between subsystems, as evidenced by its non-negativity and monotonicity under
local operations. Furthermore, the RMI is UV finite and well-defined in the
continuum limit. We develop a replica path integral approach for the RMI in
quantum field theories and evaluate it explicitly in 1+1D conformal field
theory using twist fields. We prove that it bounds connected correlation
functions and check our results against exact numerics in the massless free
fermion theory.
