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Einstein manifolds as yang-mills instantons

Title
Einstein manifolds as yang-mills instantons
Authors
Oh J.J.Yang H.S.
Ewha Authors
양현석
Issue Date
2013
Journal Title
Modern Physics Letters A
ISSN
0217-7323JCR Link
Citation
vol. 28, no. 21
Indexed
SCI; SCIE; SCOPUS WOS scopus
Abstract
It is well known that Einstein gravity can be formulated as a gauge theory of Lorentz group where spin connections play a role of gauge fields and Riemann curvature tensors correspond to their field strengths. One can then pose an interesting question: What is the Einstein equation from the gauge theory point of view? Or equivalently, what is the gauge theory object corresponding to Einstein manifolds? We show that the Einstein equations in four dimensions are precisely self-duality equations in Yang-Mills gauge theory and so Einstein manifolds correspond to Yang-Mills instantons in SO(4) = SU(2)L × SU(2)R gauge theory. Specifically, we prove that any Einstein manifold with or without a cosmological constant always arises as the sum of SU(2)L instantons and SU(2)R anti-instantons. This result explains why an Einstein manifold must be stable because two kinds of instantons belong to different gauge groups, instantons in SU(2)L and anti-instantons in SU(2)R, and so they cannot decay into a vacuum. We further illuminate the stability of Einstein manifolds by showing that they carry nontrivial topological invariants. © World Scientific Publishing Company.
DOI
10.1142/S0217732313500971
Appears in Collections:
연구기관 > 초기우주과학기술연구소 > Journal papers
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