What type of study is this?

This is a Quantitative Study study (also classified as: Experimental Study).

October 13, 2025Open Access

Dirac operators twisted by ramified Euclidean line bundles

GBGorapada BeraSimons Center for Geometry and Physics TWThomas WalpuskiHumboldt-Universität zu Berlin

Key Points

The analysis outlines how Dirac operators twisted by ramified line bundles yield new insights into harmonic spinors.
Closed extensions of Dirac operators are expressed through the Gelfand-Robbin quotient, emphasizing geometric properties.
Constructing a geometric realization of the Gelfand-Robbin quotient allows for the development of an L2 regularity theory.
Assuming specific geometric constraints, this framework could advance understanding in calibrated geometry and gauge theory.

Abstract

This article is concerned with the analysis of Dirac operators D twisted by ramified Euclidean line bundles (Z, l) -motivated by their relation with harmonic Z/2Z spinors, which have appeared in various context in gauge theory and calibrated geometry. The closed extensions of D are described in terms of the Gelfand-Robbin quotient H. Assuming that the branching locus Z is a closed cooriented codimension two submanifold, a geometric realisation of H is constructed. This, in turn, leads to an L² regularity theory.

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