Superinstanton modes

Abstract

We construct the superfield version of the instanton and investigate the zero modes using the background superfield method. A general method of generating covariant expressions for the discrete zero modes is described. It is found that the linearly independent set of superfield zero modes is not just the 8 bosonic and 4 fermionic zero modes which were expected, but also 4 further fermionic zero modes corresponding to anomalous supergauge modes — making the super-instanton measure manifestly supersymmetric.It is shown that the continuous supergauge zero modes and the positive-frequency modes can be parameterised through antichiral eigenstates of background □. In particular, this implies that background-chiral, background-antichiral, and vector superfield modes have the same spectrum of non-zero eigenvalues. These modes allow us to construct the full Green functions in the background field and projection operators onto the corresponding spaces.