tt^* Geometry, Singularity Torsion and Anomaly Formulas

2017/10/11 by Xinxing Tang, Tang, Xinxing
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.1710.03915

arxiv created 2018/05/14 · arxiv updated 2018/05/15

Abstract

This paper is concerned with the Schrödinger operators Δ_f0 and Δ_f attached to a pair (ℂⁿ, f₀) and its deformation (ℂⁿ, f), where f₀ is a non-degenerate and quasi-homogeneous polynomial on ℂⁿ 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.

Related

• Torsion type invariants of singularities
• Schrödinger equations, deformation theory and tt^*-geometry
• Weyl cohomology and the conformal anomaly in the presence of torsion
• Hodge theory and deformations of SKT manifolds
• η-invariant and flat vector bundles II