We consider the vacuum structure of two-dimensional ϕ4 theory on S1/Z2 both in the bosonic and the supersymmetric cases. When the size of the orbifold is varied, a phase transition occurs at Lc=2π/m, where m is the mass of ϕ. For L<Lc, there is a unique vacuum, while for L>Lc, there are two degenerate vacua. We also obtain the 1-loop quantum corrections around these vacuum solutions, exactly in the case of L<Lc and perturbatively for L greater than but close to Lc. Including the fermions we find that the “chiral” zero modes around the fixed points are different for L<Lc and L>Lc. As for the quantum corrections, the fermionic contributions cancel the singular part of the bosonic contributions at L=0. Then the total quantum correction has a minimum at the critical length Lc.
Physical Review D (Particles, Fields, Gravitation and Cosmology) 72(6), 065010(7pages)