Description
Defects provide powerful probes of higher-dimensional SCFTs. In general, the defect insertion gives rise to nontrivial contributions to the ground state energy and the entanglement structure. We show that these contributions are controlled by defect anomalies. In particular, we establish closed-form formulas for defect contribution to the twisted Rényi entropy.
For half-BPS surface defects in 6d $(2,0)$ SCFTs, we show that the defect supersymmetric Casimir energy and supersymmetric Rényi entropy are fixed by the defect Weyl anomaly coefficients $b$ and $d_2$. Our method combines supersymmetric localization, anomaly polynomials and holographic brane constructions, and can be extended to defects with different co-dimensions, global symmetries and bulk theories, e.g., Gukov–Witten surface defects in 4d $\mathcal{N}=4$ SYM, surface defects in 6d $(1,0)$ SCFTs, and codimension-2 defects in 6d $(2,0)$ SCFTs. This suggests universal relations between defect Weyl/’t Hooft anomalies and the defect contribution to the protected energy and entropy observables.
