Intrinsic-defect formulation of non-conformal defect entanglement entropy

Ascertain whether the defect entanglement entropy for codimension-2 monodromy defects in non-conformal maximally supersymmetric SU(N) Yang-Mills theories (specifically for p=2 and p=4) can be expressed purely in terms of defect-local observables intrinsic to the defect—rather than only as a quantity proportional to the ambient theory’s free energy—analogous to the conformal case where it is written using defect Weyl anomaly and conformal weight.

Background

The paper computes the defect entanglement entropy (dEE) for codimension-2 monodromy defects in maximally supersymmetric SU(N) Yang-Mills theories in dimensions p+1 with p=2,3,4. In the conformal case (p=3), dEE can be written as a linear combination of defect Weyl anomaly and conformal weight, consistent with known results for superconformal defects.

For non-conformal cases (p=2,4), the authors find that dEE is proportional to the free energy of the ambient theory, using a holographic renormalization scheme that relies on the AdS asymptotics in brane frame. They raise the question of whether a formulation solely in terms of intrinsic defect quantities exists in these non-conformal settings, similar to the conformal scenario.