Self-dual Yang-Mills fields in eight dimensions

Bilge, AH
Dereli, T
Kocak, S
Strongly self-dual Yang-Mills fields in even-dimensional spaces are characterised by a set of constraints on the eigenvalues of the Yang-Mills fields F-mu nu. We derive a topological bound on R(8), integral(M)(F, F)(2) greater than or equal to k integral(M) p(1)(2), where p(1) is the first Pontryagin class of the SO(n) Yang-Mills bundle, and k is a constant. Strongly self-dual Yang-Mills fields realise the lower bound.


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The covariant path integral quantization of the theory of the scalar and spinor fields interacting through the Abelian and non-Abelian Chern-Simons gauge fields in 2 + 1 dimensions is carried out using the De Witt-Fadeev-Popov method. The mathematical ill-definiteness of the path integral of theories with pure Chern-Simons' fields is remedied by the introduction of the Maxwell or Maxwell-type (in the non-Abelian case) terms, which make the resulting theories super-renormalizable and guarantees their gauge-i...
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Dereli, T; Schray, J; Tucker, RW (IOP Publishing, 1996-08-21)
We demonstrate that the left (and right) invariant Maurer-Cartan forms for any semi-simple Lie group enable solutions of the Yang-Mills equations to be constructed on the group manifold equipped with the natural Cartan-Killing metric. For the unitary unimodular groups the Yang-Mills action integral is finite for such solutions. This is explicitly exhibited for the case of SU(3).
Citation Formats
A. Bilge, T. Dereli, and S. Kocak, “Self-dual Yang-Mills fields in eight dimensions,” LETTERS IN MATHEMATICAL PHYSICS, pp. 301–309, 1996, Accessed: 00, 2020. [Online]. Available: