Fermion Propagators in Type II Fivebrane Backgrounds

TL;DR

This paper calculates fermion propagators in type II fivebrane backgrounds using conformal field theory, revealing how supersymmetry is broken and confirming the absence of certain fermion propagations consistent with supergravity zero-mode arguments.

Contribution

It provides an explicit method to compute fermion propagators in fivebrane backgrounds within superstring theory, connecting world-sheet CFT calculations to spacetime properties.

Findings

Fermion propagators are explicitly calculated in the fivebrane background.

Half of the supersymmetry is spontaneously broken in this background.

No propagation of SO(4) spinor fields is observed, aligning with supergravity zero-mode predictions.

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 non-trivial 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 non-trivial ten-dimensional space-time of the fivebrane background: M^6 x W_k^(4), where W_k^(4) is the group manifold of SU(2)_k x U(1). The half of the original supersymmetry is spontaneously broken, and the space-time Lorentz symmetry SO(9,1) reduces to SO(5,1) in SO(5,1) x SO(4) \subset SO(9,1) by the fivebrane background. We find that there are no propagations of 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.