Defect entanglement entropy for superconformal monodromy defects

TL;DR

This work holographically computes the defect entanglement entropy for co-dimension two superconformal monodromy defects in $d=3,4,6$ SCFTs and shows that the universal defect contribution, $\\mathcal{C}_{\\mathcal{D}}^{(d)}$, can vary non-monotonically along defect RG flows. By expressing the defect entropy in terms of defect data such as monodromy sources $g\\mu^I$, conical deficit $n$, and defect data $h_D$, $I_D$, and $b$, the authors connect holographic observables to defect CFT characteristics across ABJM (d=3), $\mathcal{N}=4$ SYM (d=4), and the $d=6$ $\mathcal{N}=(2,0)$ theory. They derive explicit formulas for $\\mathcal{C}_{\\mathcal{D}}^{(d)}$ in each theory, relate them to $h_D$ and defect Weyl anomalies, and analyze RG flows such as ABJM$\leftrightarrow$mABJM and $\mathcal{N}=4$ to Leigh-Strassler, showing that monotonicity is not generic for defect observables. The work also refines holographic renormalization for these defects, extending previous results to include conical deficits, and provides a framework for studying more general monodromy defects holographically. Altogether, the paper clarifies how defect data control entanglement and related anomaly-like quantities in strongly coupled dCFTs and highlights subtle differences from bulk RG behavior.

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.

Figures (8)

• Figure 1: The scheme independent part of the defect entanglement entropy, $\mathcal{C}_\mathcal{D}^{(3)}$, for ABJM with $\mu_B=0$ (left) and mABJM (right) defects with $n=1$. The parameter $\kappa = \pm1$ appears here to aid in comparison with Arav:2024wyg---in this work we take $\kappa = 1$ without loss of generality.
• Figure 2: The locus of monodromy parameters at which $\mathcal{C}_\mathcal{D}^{(3)}$, for ABJM with $\mu_B=0$ (blue) and mABJM (red) defects with $n=1$ vanishes. The "allowed region" of monodromy parameters under which a flow naively might exist is given by the interior of the dashed triangle.
• Figure 3: The ratio of $\mathcal{C}_\mathcal{D}^{(3)}$ between mABJM and ABJM (with $\mu_B=0$) defects for various values of $n>1$. The monotonicity of this quantity depends on the value of $n$ characterising the conical deficit.
• Figure 4: The ratio of $\mathcal{C}_\mathcal{D}^{(4)}$ between $\mathcal{N}=4$ (with $g\mu_B = 0$) and LS defects for various values of $n\ge1$.
• Figure 5: The ratio of $\mathcal{C}^{(3)}$ between ABJM and mABJM (with $\mu_B=0$) defects for $n=1$. This quantity is greater than one for all allowed values of the monodromy sources.