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High Energy Physics - Theory, hep-th
Abstract:
We study the late-time properties of pseudo-(R\'enyi) entropy of locally
excited states in rational conformal field theories (RCFTs). The two
non-orthogonal locally excited states used to construct the transition matrix
are generated by acting different descendant operators on the vacuum. We prove
that for the cases where two descendant operators are generated by a single
Virasoro generator respectively acting on a primary operator, the late-time
excess of pseudo-entropy and pseudo-R\'enyi entropy always coincides with the
logarithmic of the quantum dimension of the corresponding primary operator.
Furthermore, we consider two linear combination operators generated by the
generic summation of Virasoro generators. We find their pseudo-R\'enyi entropy
and pseudo-entropy may get additional contributions, as the mixing of
holomorphic and anti-holomorphic parts of the correlation function enhances the
entanglement. Finally, we assert the pseudo-R\'enyi entropy and pseudo-entropy
are still the logarithmic quantum dimension of the primary operator when the
correlation function of linear combination operators can be divided into the
product of its holomorphic part and anti-holomorphic part. We offer some
examples to illustrate the phenomenon.
