NO SATURATION OF THE QUANTUM BOGOMOLNYI BOUND BY 2-DIMENSIONAL N=1 SUPERSYMMETRIC SOLITONS

We reanalyse the question whether the quantum Bogomolnyi bound is satu rated in the two-dimensional supersymmetric kink and sine-Gordon model s. Our starting point is the usual expression for the one-loop correct ion to the mass of a soliton in terms of sums over zero-point energies , To regulate these sums, most authors put the system in a box with su itable boundary conditions, and impose an ultraviolet cut-off. We dist inguish between an energy cut-off and a mode-number cut-off, and show that they lead to different results. We claim that only the mode cut-o ff yields correct results, and only if one considers exactly the same number of bosonic and fermionic modes in the total sum over bound-stat e and zero-point energies. To substantiate this claim, we show that in the sine-Gordon model only the mode cut-off yields a result for the q uantum soliton mass that is consistent with the exact result for the s pectrum as obtained by Dashen et al. from quantising the so-called bre ather solution. In the supersymmetric case, our conclusion is that con trary to previous claims the quantum Bogomolnyi bound is not saturated in any of the two-dimensional models considered. (C) 1997 Elsevier Sc ience B.V.