Membrane instantons and non-perturbative effects in AdS₄/CFT₃

@misc{kurlyand2026membrane,
  title = {{Membrane instantons and non-perturbative effects in $\mathrmAdS_4/\mathrmCFT_3$}},
  author = {Stefan A. Kurlyand},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2606.19467},
  eprint = {2606.19467},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.19467},
}

TY  - UNPB
TI  - Membrane instantons and non-perturbative effects in AdS_4/CFT_3
AU  - Stefan A. Kurlyand
PY  - 2026
DA  - 2026/09/09
PB  - arXiv
DO  - 10.48550/arxiv.2606.19467
UR  - https://arxiv.org/abs/2606.19467
AB  - We study Euclidean M2-brane instantons in Freund-Rubin backgrounds AdS_4× Y_7. For a seven-dimensional weak G_2 manifold Y_7, we show that the BPS condition for an M2-brane wrapping a three-cycle Σ⊂ Y_7 is equivalent to the associativity condition with respect to the nearly parallel G_2-structure. When Y_7 is Sasaki-Einstein, we identify a special class of BPS M2-branes that preserve both real internal Killing spinors and correspond to invariant three-dimensional submanifolds inheriting a Sasakian structure. We analyse the quadratic fluctuations around BPS M2-brane instantons in these backgrounds. For the special class of M2-branes in Sasaki-Einstein manifolds, the fluctuation problem reduces to transversely elliptic complexes, and the one-loop partition function can be expressed in terms of the corresponding equivariant indices. We then apply the index formula for the one-loop partition function to invariant M2-branes in S^7/ℤ_k, recovering the known result for the S^3/ℤ_k instantons and discussing more general invariant BPS cycles. As a further application, we consider M2-brane instantons with S^3-quotient worldvolumes in the (p,q)-model geometry.
ER  -