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Title: The duality between two-index potentials and the non-linear sigma model in field theory
Author: Zois, Ioannis
ISNI:       0000 0001 3578 0447
Awarding Body: University of Oxford
Current Institution: University of Oxford
Date of Award: 1996
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We interpret the generalised gauge symmetry introduced in string theory and M-Theory as a special case of Grothendieck's stability equivalence relation in the definition of the 0th K-group and we calculate the Euler number of the elliptic de Rham complex twisted by a flat connection. Then using Polyakov's classical equivalence of flat bundles with non-linear sigma models we define a new topological invariant for foliations using techniques from noncommutative geometry, in particular the Connes' pairing between K-Theory and cyclic cohomology. This new invariant classifies foliations up to Morita equivalence.
Supervisor: Tsou, Sheung Tsun Sponsor: EPSRC ; A.S. Onassis Public Benefit Foundation ; A.G. Leventis Foundation
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Geometry ; Algebraic topology ; Theoretical physics ; Foliations ; K-Theory ; Index Theory ; Global Analysis ; M-Theory ; Superstring theory