Calabi-Yau Manifolds, Hermitian Yang-Mills Instantons, and Mirror Symmetry by Hyun Seok Yang, Sangheon Yun

“…We explore how the doubling is related to the mirror symmetry of Calabi-Yau manifolds. Via the gauge theory formulation of six-dimensional Riemannian manifolds, we show that the curvature tensor of a Calabi-Yau manifold satisfies the Hermitian Yang-Mills equations on the Calabi-Yau manifold. …”
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Embedding Feynman integral (Calabi-Yau) geometries in weighted projective space by Jacob L. Bourjaily, Andrew J. McLeod, Cristian Vergu, Matthias Volk, Matt von Hippel, Matthias Wilhelm

“…Abstract It has recently been demonstrated that Feynman integrals relevant to a wide range of perturbative quantum field theories involve periods of Calabi-Yau manifolds of arbitrarily large dimension. While the number of Calabi-Yau manifolds of dimension three or higher is considerable (if not infinite), those relevant to most known examples come from a very simple class: degree-2k hypersurfaces in k-dimensional weighted projective space WP1,...,1,k . …”
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Notes on integrating out M2 branes by Jarod Hattab, Eran Palti

“…Abstract Integrating out supersymmetric M2 branes wrapped on two-cycles in Calabi–Yau manifolds is an important calculation: it allows the determination of, and in some ways defines, the free energy of topological strings. …”
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BPS States, Crystals, and Matrices by Piotr Sułkowski

“…We review free fermion, melting crystal, and matrix model representations of wall-crossing phenomena on local, toric Calabi-Yau manifolds. We consider both unrefined and refined BPS counting of closed BPS states involving D2- and D0-branes bound to a D6-brane, as well as open BPS states involving open D2-branes ending on an additional D4-brane. …”
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