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arxiv 2006.02435 v2 pith:JRIPOQ2S submitted 2020-06-03 hep-th math.AGmath.DG

Shamit Kachru , Arnav Tripathy , Max Zimet This is my paper · ORCID
classification hep-thmath.AGmath.DG
keywords constructionmetricsahlerarxivcasecompactifiedcomputingcontains
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abstract

We provide an explicit construction of Ricci-flat K3 metrics. It employs the technology of D-geometry, which in the case of interest is equivalent to a hyper-K\"ahler quotient. We relate it to the construction of arXiv:1810.10540, and in particular show that it contains the solution to the BPS state counting problem (that of computing the BPS index of a heterotic little string theory compactified on $T^2$) discussed therein, which is the data needed for this second construction of K3 metrics.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Balanced Metrics Know About SYZ

    hep-th 2026-07 conditional novelty 6.0 of 10

    Ambient balanced metric coefficients on Calabi-Yau manifolds decay as |ψ|^{-f(α)} near the large complex structure limit, and the exponent function's Legendre transform gives the dual tropical potential expected from SYZ.

  2. Hyper-K\"ahler manifolds from Riemann-Hilbert problems I: Ooguri-Vafa-like model geometries

    math.DG 2025-01 conditional novelty 6.0 of 10

    The authors rigorously build local hyper-Kähler model geometries, generalizing Ooguri-Vafa and multi-Ooguri-Vafa examples, from the Gaiotto-Moore-Neitzke Riemann-Hilbert formalism.

  3. Symbolic Approximations to Ricci-flat Metrics Via Extrinsic Symmetries of Calabi-Yau Hypersurfaces

    hep-th 2024-12 conditional novelty 6.0 of 10

    The paper proposes that Calabi-Yau flat metrics inherit extra symmetries from the surrounding space, and uses this to build compact symbolic approximations and exact expressions on special loci.

  4. What to do with a Ricci-flat Calabi--Yau metric?

    hep-th 2026-05 unverdicted novelty 3.0 of 10

    Numerical Ricci-flat Calabi–Yau metrics turn string compactifications from topological existence statements into computable geometries, unlocking normalized couplings, spectra, and metric-level tests of mirror symmetry.

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