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Just as exactly marginal operators allow to deform a conformal field theory along the space of theories known as the conformal manifold, appropriate operators on conformal defects allow for deformations of the defects. A setup that guarantees exactly marginal defect operators in theories with extended supersymmetry are defects that break the R-symmetry group. In that case the conformal manifold is the symmetry breaking coset and its Zamolodchikov metric is expressed as the two point function of the exactly marginal operator. As the Riemann tensor on the conformal manifold can be expressed as an integrated correlator of the marginal operators, we find an exact relation to the curvature of the coset space. We examine in detail the case of the 1/2 BPS Maldacena-Wilson loop in N = 4 SYM, which breaks SO(6) → SO(5) and the 1/2 BPS surface operator of the 6d N = (2, 0) theory with SO(5) → SO(4) breaking. We verify this identity against known 4-point functions, previously derived from AdS/CFT and the conformal bootstrap.

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