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The 6d $\mathcal{N}=(2,0)$ theory has natural surface operator observables,which are akin in many ways to Wilson loops in gauge theories. We propose adefinition of a "locally BPS" surface operator and study its conformalanomalies, the analog of the conformal dimension of local operators. We studythe abelian theory and the holographic dual of the large $N$ theory refiningpreviously used techniques. Introducing non-constant couplings to the scalarfields allows for an extra anomaly coefficient, which we find in both cases tobe related to one of the geometrical anomaly coefficients, suggesting a generalrelation due to supersymmetry. We also comment on surfaces with conicalsingularities.

Surface operators in the 6d $\mathcal{N} = (2,0)$ theory