Quaternionic Multi - S4S^4 Approximately Equal to HP-1 Gravitational and Chiral Instantons

Sep, 1979
5 pages
Published in:
  • Phys.Lett.B 88 (1979) 282-286
  • Published: 1979
Report number:
  • COO-3075-236

Citations per year

198019902000201020207210
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