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Abstract

In this work, we study the real-time evolution of pseudo-(R\'enyi) entropy, a
generalization of entanglement entropy, in two-dimensional conformal field
theories (CFTs). We focus on states obtained by acting primary operators
located at different space points or their linear combinations on the vacuum.
We show the similarities and differences between the pseudo-(R\'enyi) entropy
and entanglement entropy. For excitation by a single primary operator, we
analyze the behaviors of the 2nd pseudo-R\'enyi entropy in various limits and
find some symmetries associated with the subsystem and the positions of the
insertion operators. For excitation by linear combinations, the late time limit
of the $n$th pseudo-R\'enyi entropy shows a simple form related to the
coefficients of the combinations and R\'enyi entropy of the operators, which
can be derived by using the Schmidt decomposition. Further, we find two kinds
of particular spatial configurations of insertion operators in one of which the
pseudo-(R\'enyi) entropy remains real throughout the time evolution.