In JT gravity with higher-derivative scalar couplings, the geometric entropy flow generalizes the BCP kink transformation by adding delta-function singularities in the dilaton and matter fields.
The Action of Geometric Entropy in Topologically Massive Gravity
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Due to the presence of a gravitational anomaly in topologically massive gravity (TMG), the geometric entropy is no longer simply the Hubeny-Rangamani-Takayanagi (HRT) area; instead, it is given by the HRT area plus an anomalous contribution. We study the action of this geometric entropy on the covariant phase space of classical solutions for TMG with matter fields whose action is algebraic in the metric. The result agrees precisely with the action of HRT area operators in Einstein-Hilbert gravity given in arXiv:2203.04270, i.e., it is a boundary-condition-preserving kink transformation. Furthermore, we show our result to be consistent with direct computations of semiclassical commutators of geometric entropies in pure TMG spacetimes asymptotic to planar AdS, as computed in arXiv:2206.00027.
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Geometric Entropies and their Hamiltonian Flows
In JT gravity with higher-derivative scalar couplings, the geometric entropy flow generalizes the BCP kink transformation by adding delta-function singularities in the dilaton and matter fields.