Quaternionic Multi - Approximately Equal to HP-1 Gravitational and Chiral Instantons
Sep, 19795 pages
Published in:
- Phys.Lett.B 88 (1979) 282-286
- Published: 1979
Report number:
- COO-3075-236
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Abstract: (Elsevier)
Compact multi S 4 gravitational instantons (positive definite metric solutions to Einstein's equations with a Λ term) are found in terms of quaternionic harmonic mappings x n : S 4 → S 4 . The manifold is the euclidean de Sitter space S 4 ≃ HP(1) with Euler-Poincaré index I E = n and Pontryagin index I P = 0. The metric can be alternatively seen as the induced metric of a Kähler HP(1) chiral field space, these same solutions then correspond to all multi chiral instantons in a general covariant quaternionic HP(1) ≃ SO(5)/SO(4) ≃ Sp(2)/Sp(1) × Sp(1) nonlinear σ-model of de Alfaro et al. They are the quaternionic counterparts of the harmonic instanton maps of the 2-dimensional CP(1) ≃ SO(3)/SO(2) ≃ SU(2)/U(1) σ-model.- GRAVITATION
- FIELD EQUATIONS: INSTANTON
- SYMMETRY: CHIRAL
- ALGEBRA: QUATERNION
- FIELD THEORY: NONLINEAR
- FIELD THEORETICAL MODEL: SIGMA
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