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arXiv:2510.01655

Entanglement entropy between tangent balls in CFT$_D$

Jiankun Li, Li Song

Published Oct 2, 2025• 0 citations
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Abstract

We apply the universal method developed in \cite{Jiang:2025jnk} to compute the entanglement entropy between two tangent balls in CFT$_D$. When taking the radius of one ball to infinity, it gives the entanglement entropy between a ball and its tangent half plane. In two-dimensional case, this configuration is equivalent to the entanglement in boundary conformal field theory (BCFT) between the negative half-axis and an interval ending on the boundary.

DOI
10.48550/arxiv.2510.01655

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Entanglement entropy between tangent balls in CFTD_DD​
We apply the universal method developed in \cite{Jiang:2025jnk} to compute the entanglement entropy between two tangent balls in CFTD_DD​. When taking the radius of one ball to infinity, it gives the entanglement entropy between a ball and its tangent half plane. In two-dimensional case, this configuration is equivalent to the entanglement in boundary conformal field theory (BCFT) between the negative half-axis and an interval ending on the boundary.
In this paper, we use entanglement entropy as a tool to explore the universal properties of conformal field theories (CFTs) dual to extremal BTZ black holes. We demonstrate that the entanglement entropies computed in the CFTs at the boundary of the extremal BTZ and the boundary of the near-horizon limit of the extremal BTZ are in perfect agreement and have the form appropriate to a two-dimensional CFT with only the chiral part excited and the antichiral in the ground state. Furthermore, we analyze the universal limits of the entanglement entropy and recover the correct value of the thermal entropy for large entangling intervals and the first-law-like relation for the small interval.
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Inspired by the holographic computation of large interval entanglement entropy of two-dimensional (2D) conformal field theory at high temperature, it was proposed that the thermal entropy is related to the entanglement entropy as ${S}_{th}=\underset{l\ensuremath{\rightarrow}0}{\mathrm{lim}}({S}_{EE}(R\ensuremath{-}l)\ensuremath{-}{S}_{EE}(l))$. In this paper, we prove this relation for 2D CFT with a discrete spectrum in two different ways. Moreover, we discuss this relation for a 2D noncompact free scalar, which is a gapless CFT with continuous spectrum. We show that it could be recovered, after appropriately regularizing the theory.
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We analyze how excitations affect the entanglement entropy for an arbitrary entangling interval in a 2d conformal field theory (CFT) using the holographic entanglement entropy techniques as well as direct CFT computations. We introduce the excitation entanglement entropy ${\mathrm{\ensuremath{\Delta}}}_{h}S$, the difference between the entanglement entropy generic excitations and their arbitrary conformal descendants denoted through hhh. The excitation entanglement entropy, unlike the entanglement entropy, is a finite quantity (independent of the cutoff), and hence a good physical observable. We show that the excitation entanglement entropy for any given interval is uniquely specified by a local second order differential equation sourced by the one point function of the energy momentum tensor computed in the excited background state, and two boundary and smoothness conditions. We analyze low and high temperature behavior of the excitation entanglement entropy and show that ${\mathrm{\ensuremath{\Delta}}}_{h}S$ grows as a function of temperature. We prove an ``integrated positivity'' for the excitation entanglement entropy, that although ${\mathrm{\ensuremath{\Delta}}}_{h}S$ can be positive or negative, its average value is always positive. We also discuss the mutual and multipartite information and (strong) subadditivity inequality in the presence of generic excitations and their conformal descendants.
In this paper we calculate the entanglement entropy for topological interfaces in rational conformal field theories for the case where the interface lies at the boundary of the entangling interval and for the case where it is located in the center of the entangling interval. We compare the results to each other and also to the recently calculated left/right entropy of a related BCFT. We also comment of the entanglement entropies for topological interfaces for a free compactified boson and Liouville theory.