Recent Developments in Heterotic Moduli

Javier José Murgas Ibarra; Eirik Eik Svanes

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arXiv · 2409.16524

Recent Developments in Heterotic Moduli

Javier José Murgas Ibarra·Eirik Eik Svanes

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Abstract

We review recent results for heterotic moduli and the Hull--Strominger system. In particular, we discuss mathematical properties of the recently derived deformation operator $\bar D$ associated to the deformation complex of heterotic $SU(3)$ solutions. We review results on Serre duality, showing that the operator has a vanishing index, and discuss a notion of Čech cohomology and a particular instance of a Dolbeault theorem for $\bar D$. Specifically, the cohomology parametrising infinitesimal deformations is isomorphic to the first Čech cohomology of an associated cochain complex. This will be useful for future research, as it provides a more algebraic handle on the heterotic moduli problem, which is useful for understanding notions of stability, geometric invariants, and enumerative geometry for the Hull--Strominger system.

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Javier José Murgas Ibarra, Eirik Eik Svanes. 2024-10-01. Recent Developments in Heterotic Moduli. https://arxiv.org/abs/2409.16524

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