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

Abstract

Abstract We consider a $$ \frac{1}{2} $$ 1 2 -BPS solution for a D3 brane probe in AdS5× S5 that has world-volume geometry of AdS3× S1. It intersects the boundary over a surface that represents a dimension 2 defect in the boundary $$ \mathcal{N} $$ N = 4 SYM theory. The effective action of the probe brane is proportional to the logarithmically divergent volume of AdS3 and may thus be interpreted as computing conformal anomaly of supersymmetric S2 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 $$ \frac{1}{2} $$ 1 2 -BPS M5 brane probe solution in AdS7× S4 with the world-volume geometry of AdS5× S1 that represents a dimension 4 defect in the boundary (2,0) 6d theory. Here the classical M5 brane action computes the leading order N2 term in a-anomaly of the supersymmetric S4 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 S4 defect a-anomaly coefficient.