Clash of discrete symmetries for the supersymmetric kink on a circle

Abstract

We consider the N=1 supersymmetric kink on a circle, i.e., on a finite interval with boundary or transition conditions which are locally invisible. For Majorana fermions, the single-particle Dirac Hamiltonian as a differential operator obeys simultaneously the three discrete symmetries of charge conjugation, parity, and time reversal. However, no single locally invisible transition condition can satisfy all three. When calculating sums over zero-point energies by mode number regularization, this gives a new rationale for a previous suggestion that one has to average over different choices of boundary conditions, such that for the combined set all three symmetries are obeyed. In particular it is shown that for twisted periodic or twisted antiperiodic boundary conditions separately both parity and time reversal are violated in the kink sector, as manifested by a delocalized momentum that cancels only in the average.

REVTeX4, 15 pages, 1 figure; v3: minor corrections and additions, 2 further references

References in corpus (10)

• One-loop surface tensions of (supersymmetric) kink domain walls from dimensional regularization
• The anomaly in the central charge of the supersymmetric kink from dimensional regularization and reduction
• Mode regularization of the susy sphaleron and kink: zero modes and discrete gauge symmetry
• Local Casimir Energy For Solitons
• CPT anomaly: a rigorous result in four dimensions
• CP breaking in lattice chiral gauge theories
• Once more on the BPS bound for the susy kink
• Quantization of supersymmetric solitons
• Torsion, topology and CPT anomaly in two-dimensional chiral U(1) gauge theory
• Subtleties in CPT-Transformation for Majorana fermions

Cited by in corpus (6)

• Nonvanishing quantum corrections to the mass and central charge of the N=2 vortex and BPS saturation
• The anomaly in the central charge of the supersymmetric kink from dimensional regularization and reduction
• Local Casimir Energy For Solitons
• Quantum Mass and Central Charge of Supersymmetric Monopoles - Anomalies, current renormalization, and surface terms
• Boundary Terms in Supergravity and Supersymmetry
• Comment on `One Loop Renormalization of Soliton Quantum Mass Corrections in 1+1 Dimensional Scalar Field Theory Models' (Phys. Lett. B542 (2002) 282 [hep-th/0206047])