Topological symmetry breaking of self--interacting fractional Klein--Gordon field on toroidal spacetime

Quartic self–interacting fractional Klein–Gordon scalar massive and massless field theories on toroidal spacetime are studied. The effective potential and topologically generated mass are determined using zeta function regularization technique. Renormalization of these quantities are derived. Conditions for symmetry breaking are obtained analytically. Simulations are carried out to illustrate regions or values of compactified dimensions where symmetry breaking mechanisms appear.