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arXiv:2511.22695

Defect entanglement entropy for superconformal monodromy defects

Conti, Andrea, Yolanda Lozano, Rogdakis, Filippos, C. A. Rosen

Published Nov 27, 2025• 1 citation
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Abstract

We compute the defect entanglement entropy for co-dimension two superconformal monodromy defects in well known maximally symmetric holographic theories of various dimension. In each case we explicitly relate the universal part of the defect entanglement entropy to field theory data characterising the defect conformal field theory. We provide evidence that, unlike in the bulk theories in which the defects reside, the universal part of the defect entanglement entropy does not necessarily decrease along a renormalisation group flow.

DOI
10.48550/arxiv.2511.22695

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A bstract We compute the defect entanglement entropy for co-dimension two superconformal monodromy defects in well known maximally symmetric holographic theories of various dimension. In each case we explicitly relate the universal part of the defect entanglement entropy to field theory data characterising the defect conformal field theory. We provide evidence that, unlike in the bulk theories in which the defects reside, the universal part of the defect entanglement entropy does not necessarily decrease along a renormalisation group flow.
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Abstract We study co-dimension two monodromy defects in theories of conformally coupled scalars and free Dirac fermions in arbitrary d dimensions. We characterise this family of conformal defects by computing the one-point functions of the stress-tensor and conserved current for Abelian flavour symmetries as well as two-point functions of the displacement operator. In the case of d = 4, the normalisation of these correlation functions are related to defect Weyl anomaly coefficients, and thus provide crucial information about the defect conformal field theory. We provide explicit checks on the values of the defect central charges by calculating the universal part of the defect contribution to entanglement entropy, and further, we use our results to extract the universal part of the vacuum Rényi entropy. Moreover, we leverage the non-supersymmetric free field results to compute a novel defect Weyl anomaly coefficient in a d = 4 theory of free N \mathcal{N} N N = 2 hypermultiplets. Including singular modes in the defect operator product expansion of fundamental fields, we identify notable relevant deformations in the singular defect theories and show that they trigger a renormalisation group flow towards an IR fixed point with the most regular defect OPE. We also study Gukov-Witten defects in free d = 4 Maxwell theory and show that their central charges vanish.
We study the defect contribution to the entanglement entropy of a spherical region centred on four-dimensional superconformal RG interfaces. These interfaces are supersymmetric codimension one defects separating the Leigh--Strassler SCFT vacuum and the N=4\mathcal{N}=4N=4 SYM theory deformed by spatially varying mass terms. Exploiting the holographic dual to these interfaces, we extract a cutoff-independent interface contribution to the entanglement entropy, CI\mathcal{C}^ICI. We quantify the non-trivial dependence of CI\mathcal{C}^ICI on the supersymmetric mass deformation, and observe a scaling regime for large deformations. We further relate CI\mathcal{C}^ICI to the renormalized on-shell action and the stress-tensor one-point function of the interface theory. Our results provide the first fully backreacted holographic computation of this entanglement quantity for superconformal RG interfaces in more than two dimensions.
Abstract We explore a C-theorem in defect conformal field theories (DCFTs) that unify all the known conjectures and theorems until now. We examine as a candidate C-function the additional contributions from conformal defects to the sphere free energy and the entanglement entropy across a sphere in a number of examples including holographic models. We find the two quantities are equivalent, when suitably regularized, for codimension-one defects (or boundaries), but differ by a universal constant term otherwise. Moreover, we find in a few field theoretic examples that the sphere free energy decreases but the entanglement entropy increases along a certain renormalization group (RG) flow triggered by a defect localized perturbation which is assumed to have a trivial IR fixed point without defects. We hence propose a C-theorem in DCFTs stating that the increment of the regularized sphere free energy due to the defect does not increase under any defect RG flow. We also provide a proof of our proposal in several holographic models of defect RG flows.
We study whether the relations between the Weyl anomaly, entanglement entropy (EE), and thermal entropy of a two-dimensional (2D) conformal field theory (CFT) extend to 2D boundaries of 3D CFTs, or 2D defects of D≥3 CFTs. The Weyl anomaly of a 2D boundary or defect defines two or three central charges, respectively. One of these, b, obeys a c theorem, as in 2D CFT. For a 2D defect, we show that another, d_{2}, interpreted as the defect's "conformal dimension," must be non-negative if the averaged null energy condition holds in the presence of the defect. We show that the EE of a sphere centered on a planar defect has a logarithmic contribution from the defect fixed by b and d_{2}. Using this and known holographic results, we compute b and d_{2} for 1/2-Bogomol'nyi-Prasad-Sommerfield surface operators in the maximally supersymmetric (SUSY) 4D and 6D CFTs. The results are consistent with b's c theorem. Via free field and holographic examples we show that no universal "Cardy formula" relates the central charges to thermal entropy.