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It is well-known that Calabi-Yau manifolds are popular for compactifications of six of the ten dimensions in superstring theory. However, I am not aware of any other applications in physics. Do they appear in other fields than string theory? If so, are there physical observables that depend on them in any way?

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  • $\begingroup$ Not sure about calabi yau manifolds specifically but for example the Kähler structure of manifolds comes up in the quantization of coadjoint orbits see e.g. the application of virasoro coadjont orbits to calculating the schwarzian path integral which shows up as a low energy limit of the SYK model or equivalently as the near horizon dynamics of near extremal black holes $\endgroup$
    – Thomas Tappeiner
    Commented Sep 17 at 15:25

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I believe that there has been a recent example in gravitational wave physics actually. There, a CY 3-fold has come up in the integrals that one needs to evaluate when looking at the scattering of black holes in the so called WQFT framework. The paper where this is discussed is here

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Some scattering calculations in particle theory involve integration over Calabi-Yau spaces (example).

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