# Do instantons support quantum bound states?

When one quantizes a scalar in the 1+1 dimensions in the kink background of a double well potential, one finds a spectrum that includes: (1) a zero mode corresponding to the classical particle position, (2) a bound state localized on the kink, and (3) the continuum of states analogous to those found in the trivial background.

When we quantize a non-Abelian gauge theory on an instanton background, are there analogs of the bound state (#2 above)? If so, how do they appear perturbatively in my Feynman rules? If not, how can we see that the instanton is really very different from the kink?

Thanks!

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For the pure e.g. $d=4$ gauge theory instanton and gauge field perturbations around it, there is no negative mode – the counterpart of the bound state. It's the only one among the 3 classes that is absent here.