No saturation of the quantum Bogomolnyi bound by two-dimensional supersymmetric solitons

Details No saturation of the quantum Bogomolnyi bound by two-dimensional supersymmetric solitons No saturation of the quantum Bogomolnyi bound by two-dimensional supersymmetric solitons

1997-07-18

arxiv.org/abs/hep-th/9707163v1

Nucl.Phys. B508 (1997) 449-467

Physics

High Energy Physics

High Energy Physics - Theory

23 pages, LATeX

Scientific paper

10.1016/S0550-3213(97)00625-1

We reanalyse the question whether the quantum Bogomolnyi bound is saturated in the two-dimensional supersymmetric kink and sine-Gordon models. Our starting point is the usual expression for the one-loop correction 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 suitable boundary conditions, and impose an ultraviolet cut-off. We distinguish 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-off yields correct results, and only if one considers exactly the same number of bosonic and fermionic modes in the total sum over bound-state 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 quantum soliton mass that is consistent with the exact result for the spectrum as obtained by Dashen et al. from quantising the so-called breather solution. In the supersymmetric case, our conclusion is that contrary to previous claims the quantum Bogomolnyi bound is not saturated in any of the two-dimensional models considered.

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