2-loop free energy of M2 brane in AdS7 × S4 and surface defect anomaly in (2,0) theory

A bstract $\frac{1}{2}$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> mml:mfrac mml:mn1</mml:mn> mml:mn2</mml:mn> </mml:mfrac> </mml:math> -BPS surface operator viewed as a conformal defect in rank N 6d (2,0) theory is expected to have a holographic description in terms of a probe M2 brane wrapped on AdS 3 in the AdS 7 × S 4 M-theory background. The M2 brane has the effective tension T 2 = $\frac{2}{\pi }$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:m