We discuss testing AdS/CFT correspondence between U(N)ₖ × U(N)₋ₖ Chern-Simons-matter 3d gauge theory and M-theory in AdS_4× S⁷/ Zₖ background. We show that the quantum M2 brane partition function expanded near the corresponding classical solution matches the localization predictions on the gauge theory side in the case of BPS Wilson loop expectation value and instanton corrections to free energy.
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A.A. Tseytlin (2024) studied this question.
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