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Non-perturbative decay of Non-Abelian hair
We construct a solution of Heterotic supergravity which interpolates between
two different AdS geometries corresponding to the
near-horizon limits of two 5-dimensional black holes, only one of which has
non-Abelian hair. This solution can be used to estimate the amplitude of
probability of the non-perturbative decay of the gauge 5-brane responsible for
the non-Abelian hair into eight solitonic 5-branes by evaluating its Euclidean
action. The Wick rotation of this solution poses several problems which we
argue can be overcome by using a non-extremal off-shell (NEOS) deformation of
the solution. This NEOS field configuration can be Wick rotated straight away
and its Euclidean action can be computed for any value of the deformation
parameter. The Euclidean result can then be anti-Wick-rotated and its extremal
limit gives the Euclidean action of the original solution, which turns out to
be one half of the difference between the entropies of the 5-dimensional black
holes.Comment: Few typos corrected. Two references and a footnote added. Version to
be published in JHE
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