Semiclassical quantization of M5 brane probes wrapped on ${\text{AdS}}_3\times S^3$ and defect anomalies

Abstract

We consider two supersymmetric M5 brane probe solutions in ${\text{AdS}}_7\times S^4$ and one in ${\text{AdS}}_4\times S^7$ that all have the ${\text{AdS}}_3\times S^3$ world-volume geometry. The values of the classical action of the first two M5 probes (with $S^3$ in ${\text{AdS}}_7$ or in $S^4$) are related to the leading $N^2$ parts in the anomaly b-coefficient in the (2,0) theory corresponding to a spherical surface defect in symmetric or antisymmetric $SU(N)$ representations. We present a detailed computation of the corresponding one-loop M5 brane partition functions finding that they vanish (in a particular regularization). This implies the vanishing of the order $N^0$ part in the b-anomaly coefficients, in agreement with earlier predictions for their exact values. It remains, however, a puzzle of how to reproduce the non-vanishing order $N$ terms in these coefficients within the semiclassical M5-brane probe setup.

48 pages. v3: minor changes

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