This paper studies the space of L² harmonic forms and L² harmonic spinors on Taub-bolt, a Ricci-flat Riemannian 4-manifold of ALF type. We prove that the space of harmonic square-integrable 2-forms on Taub-bolt is 2-dimensional and construct a basis. We explicitly find all L² zero modes of D̸ A , the Dirac operator twisted by an arbitrary L² harmonic connection A, and independently compute the index of D̸ A . We compare our results with those known in the case of Taub-NUT and Euclidean Schwarzschild as these manifolds present interesting similarities with Taub-bolt. In doing so, we generalise known results concerning harmonic spinors on Euclidean Schwarzschild.

Harmonic forms and spinors on the Taub-bolt space

Franchetti G
2019-01-01

Abstract

This paper studies the space of L² harmonic forms and L² harmonic spinors on Taub-bolt, a Ricci-flat Riemannian 4-manifold of ALF type. We prove that the space of harmonic square-integrable 2-forms on Taub-bolt is 2-dimensional and construct a basis. We explicitly find all L² zero modes of D̸ A , the Dirac operator twisted by an arbitrary L² harmonic connection A, and independently compute the index of D̸ A . We compare our results with those known in the case of Taub-NUT and Euclidean Schwarzschild as these manifolds present interesting similarities with Taub-bolt. In doing so, we generalise known results concerning harmonic spinors on Euclidean Schwarzschild.
2019
Franchetti, G
File in questo prodotto:
File Dimensione Formato  
9.2019-Franchetti-hstb.pdf

non disponibili

Tipologia: Versione finale editoriale
Licenza: NON PUBBLICO - accesso privato/ristretto
Dimensione 497.24 kB
Formato Adobe PDF
497.24 kB Adobe PDF   Visualizza/Apri   Richiedi una copia
Harmonic forms and spinors_manuscript.pdf

accesso aperto

Tipologia: Documento in Post-print
Licenza: Creative commons
Dimensione 293.97 kB
Formato Adobe PDF
293.97 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/1269317
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 4
  • ???jsp.display-item.citation.isi??? 4
social impact