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arXiv · 1710.03915

$tt^*$ Geometry, Singularity Torsion and Anomaly Formulas

Xinxing Tang
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Abstract

This paper is concerned with the Schrödinger operators $Δ_{f_0}$ and $Δ_f$ attached to a pair $(\mathbb{C}^n, f_0)$ and its deformation $(\mathbb{C}^n, f)$, where $f_0$ is a non-degenerate and quasi-homogeneous polynomial on $\mathbb{C}^n$ and $f$ is its relevant or marginal deformation. We give the $tt^*$ geometry structure on the Hodge bundle associated to $Δ_f$, which describes the genus 0 anomaly. Next we study the corresponding singularity torsion type invariants and give the anomaly formulas for the 2nd torsion type invariant.

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Xinxing Tang. 2018-05-14. $tt^*$ Geometry, Singularity Torsion and Anomaly Formulas. https://arxiv.org/abs/1710.03915

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