Fermion propagators in type II fivebrane backgrounds

Abstract

The fermion propagators in the fivebrane background of type II superstring theories are calculated. The propagator can be obtained by explicitly evaluating the transition amplitude between two specific NS-R boundary states by the propagator operator in the nontrivial world-sheet conformal field theory for the fivebrane background. The propagator in the field theory limit can be obtained by using point boundary states. We can explicitly investigate the lowest-lying fermion states propagating in the nontrivial ten-dimensional space-time of the fivebrane background: ${M}^{6}\ifmmode\times\else\texttimes\fi{}{W}_{k}^{(4)},$ where ${W}_{k}^{(4)}$ is the group manifold of $\mathrm{SU}{(2)}_{k}\ifmmode\times\else\texttimes\fi{}\mathrm{U}(1).$ Half of the original supersymmetry is spontaneously broken, and the space-time Lorentz symmetry $\mathrm{SO}(9,1)$ reduces to $\mathrm{SO}(5,1)$ in $\mathrm{SO}(5,1)\ifmmode\times\else\texttimes\fi{}\mathrm{SO}(4)\ensuremath{\subset}\mathrm{SO}(9,1)$ by the fivebrane background. We find that there are no propagations of $\mathrm{SO}(4)$ (local Lorentz) spinor fields, which is consistent with the arguments on the fermion zero modes in the fivebrane background of low-energy type II supergravity theories.