Cm. Bender et Ka. Milton, MODEL OF SUPERSYMMETRIC QUANTUM-FIELD THEORY WITH BROKEN PARITY SYMMETRY, Physical review. D. Particles and fields, 57(6), 1998, pp. 3595-3608
Recently, it was observed that self-interacting scalar quantum field t
heories having a non-Hermitian interaction term of the form g(i phi)(2
+delta), where delta is a real positive parameter, are physically acce
ptable in the sense that the energy spectrum is real and bounded below
. Such theories possess PT invariance, but they are not symmetric unde
r parity reflection or time reversal separately. This broken parity sy
mmetry is manifested in a nonzero value for [phi] even if delta is an
even integer. This paper extends this idea to a two-dimensional supers
ymmetric quantum field theory whose superpotential is S(phi)=-ig(i phi
)(1+delta). The resulting quantum field theory exhibits a broken parit
y symmetry for all delta>0. However, supersymmetry remains unbroken, w
hich is verified by showing that the ground-state energy density vanis
hes and that the fermion-boson mass ratio is unity.