On co-dimension 2 defect anomalies in N = 4 SYM and (2, 0) theory via brane probes in AdS/CFT

A bstract We consider a 12 1 2 -BPS solution for a D3 brane probe in AdS 5 × S 5 that has world-volume geometry of AdS 3 × S 1. It intersects the boundary over a surface that represents a dimension 2 defect in the boundary N N = 4 SYM theory. The effective action of the probe brane is proportional to the logarithmically divergent volume of AdS 3 and may thus be interpreted as computing conformal anomaly of supersymmetric S 2 defect. The classical action scales as N. We compute the 1-loop correction to it due to quantum fluctuations of the D3 brane world-volume fields and compare the result to an earlier suggested expression for the defect anomaly. We also perform a similar analysis of a 12 1 2 -BPS M5 brane probe solution in AdS 7 × S 4 with the world-volume geometry of AdS 5 × S 1 that represents a dimension 4 defect in the boundary (2, 0) 6d theory. Here the classical M5 brane action computes the leading order N 2 term in a -anomaly of the supersymmetric S 4 defect. We perform a detailed computation of the 1-loop correction to the M5 brane effective action and thus provide a prediction for the subleading constant in the S 4 defect a -anomaly coefficient.