Constructs degenerating special Lagrangian two-spheres and tori in collapsing K3 surfaces that lift from affine lines on a three-dimensional base, including connections between Taub-NUT bubbles.
Fivebranes, Membranes and Non-Perturbative String Theory
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abstract
Non-perturbative instanton corrections to the moduli space geometry of type IIA string theory compactified on a Calabi-Yau space are derived and found to contain order $e^{-1/g_s}$ contributions, where $g_s$ is the string coupling. The computation reduces to a weighted sum of supersymmetric extremal maps of strings, membranes and fivebranes into the Calabi-Yau space, all three of which enter on equal footing. It is shown that a supersymmetric 3-cycle is one for which the pullback of the K\"ahler form vanishes and the pullback of the holomorphic three-form is a constant multiple of the volume element. Quantum mirror symmetry relates the sum in the IIA theory over supersymmetric, odd-dimensional cycles in the Calabi-Yau space to a sum in the IIB theory over supersymmetric, even-dimensional cycles in the mirror.
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2026 2verdicts
UNVERDICTED 2representative citing papers
BPS conditions for M2-branes wrapping cycles in weak G2 manifolds are equivalent to associativity, with one-loop effects for invariant cycles in Sasaki-Einstein orbifolds expressed via equivariant indices and recovering known S3/Zk results.
citing papers explorer
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Special Lagrangian submanifolds and circle collapse on K3
Constructs degenerating special Lagrangian two-spheres and tori in collapsing K3 surfaces that lift from affine lines on a three-dimensional base, including connections between Taub-NUT bubbles.
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Membrane instantons and non-perturbative effects in $\mathrm{AdS}_{4}/\mathrm{CFT}_{3}$
BPS conditions for M2-branes wrapping cycles in weak G2 manifolds are equivalent to associativity, with one-loop effects for invariant cycles in Sasaki-Einstein orbifolds expressed via equivariant indices and recovering known S3/Zk results.