Monodromy Defects in Maximally Supersymmetric Yang-Mills Theories from Holography

TL;DR

This work constructs holographic models of codimension-2 monodromy defects in maximally supersymmetric Yang–Mills theories for $p=2,3,4$ by wrapping D$p$-branes on spindle geometries and imposing defect boundary conditions, thereby encoding monodromies in $U(1)$ subgroups of the R-symmetry. A defect entanglement entropy prescription based on a Macpherson–Bea-type central charge is developed and renormalized, revealing that for $p=2,3,4$ the dEE is proportional to the ambient theory's free energy, while the $p=5$ case yields a circle compactification rather than a defect. The analysis employs lower-dimensional gauged supergravity truncations (4D,5D,6D) to obtain explicit defect data and boundary conditions, relating the monodromy parameters to R-symmetry and flavor holonomies and deriving SUSY-enhanced sub-sectors. Overall, the results extend holographic defect techniques to non-conformal, supersymmetric monodromy defects and highlight potential links between defect data (e.g., Weyl anomalies and conformal weights) and ambient observables in generalized conformal frameworks.

Abstract

We study three Type II supergravity solutions which are holographically dual to codimension-2 supersymmetric defects in $(p+1)$-dimensional SU($N$) maximally supersymmetric Yang-Mills ($p=2,3,4$). In all of these cases, the defects have a non-trivial monodromy for the maximal abelian subgroup for the SO($9-p$) R-symmetry. Such solutions are obtained by considering branes wrapping spindle configurations, changing the parameters (which alters the coordinate domain), and imposing suitable boundary conditions. We provide a prescription to compute the entanglement entropy of the effective theory on the defect. We find the resulting quantity to be proportional to the free energy of the ambient theory. Similar analysis is performed for the D5-brane wrapping a spindle, but we find that changing the coordinate domain does not lead to a defect solution, but rather a circle compactification.