Once more on the BPS bound for the susy kink

Abstract

We consider a new momentum cut-off scheme for sums over zero-point energies, containing an arbitrary function f(k) which interpolates smoothly between the zero-point energies of the modes around the kink and those in flat space. A term proportional to df(k)/dk modifies the result for the one-loop quantum mass M^(1) as obtained from naive momentum cut-off regularization, which now agrees with previous results, both for the nonsusy and susy case. We also introduce a new regularization scheme for the evaluation of the one-loop correction to the central charge Z^(1), with a cut-off K for the Dirac delta function in the canonical commutation relations and a cut-off Λfor the loop momentum. The result for Z^(1) depends only on whether K>Λor K<Λor K=Λ. The last case yields the correct result and saturates the BPS bound, M^(1)=Z^(1),in agreement with the fact that multiplet shortening does occur in this N=(1,1) system. We show how to apply mode number regularization by considering first a kink-antikink system, and also obtain the correct result with this method. Finally we discuss the relation of these new schemes to previous approaches based on the Born expansion of phase shifts and higher-derivative regularization.

arXiv comment28 pages, 4 figures

References in corpus (4)

• Anomaly and quantum corrections to solitons in two-dimensional theories with minimal supersymmetry
• Energy, Central Charge, and the BPS Bound for 1+1 Dimensional Supersymmetric Solitons
• Unambiguous one-loop quantum energies of 1+1 dimensional bosonic field configurations
• Derivative Expansion and Soliton Masses

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• 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])
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• The ${\varphi }^4$ Kink Mass at Two Loops
• The Supersymmetric Kink via Higher-Derivative and Momentum Cut-Off Regularization Schemes
• New results for the quantum supersymmetric kink