Superinstantons

Abstract

We show how O(g2) divergent quantum corrections to the instanton effective action may be calculated in Yang-Mills theory. We verify that these are as required by a renormalisation group analysis of the semiclassical calculation. This requires a delicate treatment of the zero modes and of the jacobian corresponding to a change of variables between these zero modes and collective coordinates.
We generalise the instanton solution to a superfield solution of N=1 super Yang-Mills theory, and describe a general method of generating covariant expressions for the discrete zero modes. It is found that the linearly independent set of zero modes contains 4 more fermionic modes than were previously expected. These are anomalous supergauge modes. We show how to parameterize the continuous supergauge zero modes and the positive frequency modes. Prom this analysis we construct the full Green functions in the background of a superinstanton and projection operators onto the corresponding spaces, we generalise our previous 0(g2) calculation to that of a superinstanton in super Yang-Mills. This allows a comparison with recent arguments that all the higher order quantum corrections in such a situation should vanish identically. We conclude that these arguments are invalid but investigate the possibility that quantum corrections do nevertheless vanish to all orders. The subtleties and complications of the cancellation mechanism make it difficult to imagine that this could be the case.

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