Abstract
We study extrema of the general conformally invariant action: S c = ∫ 1 α 2 C abcdC abcd+γR abcd ∗R abcd ∗+iθR abcd∗R abcd . We find the first examples in four dimensions of asymptotically euclidean gravitational instantons. These have arbitrary Euler number and Hirzebruch signature. Some of these instantons represent tunneling between zero-curvature vacua that are not related by small gauge transformations. Others represent tunneling between flat space and topologically non-trivial zero-energy initial data. A general formula for the one-loop determinant is derived in terms of the renormalization group invariant masses, the volume of space-time, the Euler number and the Hirzebruch signature.
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