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arXiv:2605.01150

Twist Operator BOPE and Entanglement Entropy in 2D Interface CFT

Mianqi Wang

Published May 1, 2026• 0 citations
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Abstract

We address several aspects of entanglement entropy of 2D interface CFT using the replica method. Unlike the case of boundary CFT, we consider the boundary OPE (BOPE) of the Rényi twist operator and find a boundary twist operator anchored on the interface. This approach gives the $O(1)$ contribution to the entanglement entropy in terms of the BOPE coefficients of the twist operator. We further analyze entanglement entropy of different intervals and compare our findings with previous holographic results.

DOI
10.48550/arxiv.2605.01150

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We address several aspects of entanglement entropy of 2D interface CFT using the replica method. Unlike the case of boundary CFT, we consider the boundary OPE (BOPE) of the Rényi twist operator and find a boundary twist operator anchored on the interface. This approach gives the O(1)O(1)O(1) contribution to the entanglement entropy in terms of the BOPE coefficients of the twist operator. We further analyze entanglement entropy of different intervals and compare our findings with previous holographic results.
We investigate the one-loop entanglement entropy of two short intervals with small cross ratio x on a complex plane in two-dimensional conformal field theory (CFT) using operator product expansion of twist operators. We focus on the one-loop entanglement entropy instead of the general order n Rényi entropy, and this makes the calculation much easier. We consider the contributions of stress tensor to order x 10, contributions of W 3 operator to order x 12, and contributions of W 4 operator to order x 14. The CFT results agree with the ones in gravity.
In this note, I revisit the problem of computing the entanglement entropy of a single interval in the ground state of a 2d CFT. I write the leading-order result in three different ways: once by doing the replica trick with the nnn-replicated cylinder partition function computed in the ``closed string channel"; once by computing the nnn-replicated cylinder partition function in the ``open string channel", where the entanglement entropy can be related to the density of states in a boundary CFT defined on the interval; and for holographic CFTs, once as the log of a Plancherel measure for a certain noncompact quantum group. I comment on the implications for what the Ryu-Takayanagi area term might be counting in holographic CFTs.
A bstract The entanglement entropy of intervals in 1 + 1 interface CFTs is modified in two ways compared to a CFT without interface: there is a finite boundary entropy contribution, and, for an interval with an endpoint at the interface, the coefficient of the logarithmically divergent contribution -which is usually proportional to the central charge of the CFT- is modified to an effective central charge. We show that the latter modification can be understood as a limit of the former using holographic duals of interface CFTs. Furthermore, we show that a finite “boundary entropy” contribution also appears in intervals that do not cross the interface and it is needed to ensure strong subbaditivity of the entanglement entropy.
We explore interfaces and junctions joining multiple two-dimensional conformal field theories, with the goal of calculating entanglement entropies in their presence and exploring their holographic duals. In chapter 1 we start with an overview of the three subjects, collecting various well-known results and reviewing some foundational works.In chapter 2 we calculate the holographic entanglement entropy in the presence of a conformal interface for a geometric configuration in which the entangling region lies on one side of the interface. For the supersymmetric Janus solution we find exact agreement between the holographic and conformal field theory calculation of the entanglement entropy.In chapter 3 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 left/right entropy of a related boundary conformal field theory. We also comment on the entanglement entropies for topological interfaces in Liouville theory.In chapter 4 we consider entanglement through permeable junctions of N free boson and free fermion conformal field theories. We constrain the form of the general boundary state and calculate the replicated partition functions with interface operators inserted, from which the entanglement entropy is calculated. We find the functional form of the universal and constant terms to be similar to the N=2 case, depending only of the total transmission of the junction and the unit volume of the zero mode lattice. For N>2 we see a subleading divergent term which does not depend on the parameters of the junction. For N=3 we consider some specific geometries and discuss various limits.In chapter 5 we investigate topological interfaces between three-dimensional Abelian Chern-Simons theories in the context of the AdS_3/CFT_2 correspondence. We show that it is possible to connect the topological interfaces in the bulk Chern-Simons theory to topological interfaces in the dual conformal field theory on the boundary. In addition to the [U(1)]^{2N} Chern-Simons theory on AdS_3, we show that it is possible to find boundary counter terms which lead to the N conserved currents in the dual two-dimensional conformal field theory.
Abstract In this note, we consider entanglement and Renyi entropies for spatial subsystems of a boundary conformal field theory (BCFT) or of a CFT in a state constructed using a Euclidean BCFT path integral. Holographic calculations suggest that these entropies undergo phase transitions as a function of time or parameters describing the subsystem; these arise from a change in topology of the RT surface. In recent applications to black hole physics, such transitions have been seen to govern whether or not the bulk entanglement wedge of a (B)CFT region includes a portion of the black hole interior and have played a crucial role in understanding the semiclassical origin of the Page curve for evaporating black holes. In this paper, we reproduce these holographic results via direct (B)CFT calculations. Using the replica method, the entropies are related to correlation functions of twist operators in a Euclidean BCFT. These correlations functions can be expanded in various channels involving intermediate bulk or boundary operators. Under certain sparseness conditions on the spectrum and OPE coefficients of bulk and boundary operators, we show that the twist correlators are dominated by the vacuum block in a single channel, with the relevant channel depending on the position of the twists. These transitions between channels lead to the holographically observed phase transitions in entropies.
The entanglement entropy in three-dimensional conformal field theories (CFTs) receives a logarithmic contribution characterized by a regulator-independent function a(θ) when the entangling surface contains a sharp corner with opening angle θ. In the limit of a smooth surface (θ → π), this corner contribution vanishes as a(θ) = σ(θ − π)2. In arXiv:1505.04804 , we provided evidence for the conjecture that for any d = 3 CFT, this corner coefficient σ is determined by C T , the coefficient appearing in the two-point function of the stress tensor. Here, we argue that this is an instance of a much more general relation connecting the analogous corner coefficient σ n appearing in the nth Rényi entropy and the scaling dimension h n of the corresponding twist operator. In particular, we find the simple relation h n /σ n = (n − 1)π. We show how it reduces to our previous result as n → 1, and explicitly check its validity for free scalars and fermions. With this new relation, we show that as n → 0, σ n yields the coefficient of the thermal entropy, c S . We also reveal a surprising duality relating the corner coefficients of the scalar and the fermion. Further, we use our result to predict σ n for holographic CFTs dual to four-dimensional Einstein gravity. Our findings generalize to other dimensions, and we emphasize the connection to the interval Rényi entropies of d = 2 CFTs.