Robert Wimmer

Nonvanishing quantum corrections to the mass and central charge of the N=2 vortex and BPS saturation

Abstract The one-loop quantum corrections to the mass and central charge of the N =2 vortex in 2+1 dimensions are determined using supersymmetry-preserving dimensional regularization by dimensional reduction of the corresponding N =1 model with Fayet–Iliopoulos term in 3+1 dimensions. Both the mass and the central charge turn out to have nonvanishing one-loop corrections which however are equal and thus saturate the Bogomolnyi bound. We explain BPS saturation by standard multiplet shortening arguments, correcting a previous claim in the literature postulating the presence of a second degenerate short multiplet at the quantum level.

The anomaly in the central charge of the supersymmetric kink from dimensional regularization and reduction

Abstract We show that the anomalous contribution to the central charge of the (1+1)-dimensional N =1 supersymmetric kink that is required for BPS saturation at the quantum level can be linked to an analogous term in the extra momentum operator of a (2+1)-dimensional kink domain wall with spontaneous parity violation and chiral domain wall fermions. In the quantization of the domain wall, BPS saturation is preserved by nonvanishing quantum corrections to the momentum density in the extra space dimension. Dimensional reduction from 2+1 to 1+1 dimensions preserves the unbroken N =1/2 supersymmetry and turns these parity-violating contributions into the anomaly of the central charge of the supersymmetric kink. On the other hand, standard dimensional regularization by dimensional reduction from 1 to (1− ϵ ) spatial dimensions, which also preserves supersymmetry, obtains the anomaly from an evanescent counterterm. We identify the anomaly in the ordinary central charge as an anomalous contribution to the divergence of the conformal central-charge current.

One-loop surface tensions of (supersymmetric) kink domain walls from dimensional regularization

We consider domain walls obtained by embedding the (1+1)-dimensional 4-kink in higher dimensions. We show that a suitably adapted dimensional regularization method avoids the intricacies found in other regularization schemes in both supersymmetric and non-supersymmetric theories. This method allows us to calculate the one-loop quantum mass of kinks and surface tensions of kink domain walls in a very simple manner, yielding a compact d-dimensional formula which reproduces many of the previous results in the literature. Among the new results is the non-vanishing one-loop correction to the surface tension of a (2+1)-dimensional N = 1 supersymmetric kink domain wall with chiral domain-wall fermions.

Quantum mass and central charge of supersymmetric monopoles: anomalies, current renormalization, and surface terms

We calculate the one-loop quantum corrections to the mass and central charge of N = 2 and N = 4 supersymmetric monopoles in 3+1 dimensions. The corrections to the N = 2 central charge are finite and due to an anomaly in the conformal central charge current, but they cancel for the N = 4 monopole. For the quantum corrections to the mass we start with the integral over the expectation value of the Hamiltonian density, which we show to consist of a bulk contribution which is given by the familiar sum over zero-point energies, as well as surface terms which contribute nontrivially in the monopole sector. The bulk contribution is evaluated through index theorems and found to be nonvanishing only in the N = 2 case. The contributions from the surface terms in the Hamiltonian are cancelled by infinite composite operator counterterms in the N = 4 case, forming a multiplet of improvement terms. These counterterms are also needed for the renormalization of the central charge. However, in the N = 2 case they cancel, and both the improved and the unimproved current multiplet are finite.

New developments in the quantization of supersymmetric solitons (kinks, vortices and monopoles)

We discuss the one-loop quantum corrections to the mass M and central charge Z of supersymmetric (susy) solitons: the kink, the vortex and the monopole. Contrary to previous expectations and published results, in each of these cases there are nonvanishing quantum corrections to the mass. For the N = 1 kink and the N = 2 monopole a new anomaly in Z rescues BPS saturation (M = Z); for the N = 2 vortex, BPS saturation is rescued for two reasons: (i) the quantum fluctuations of the Higgs field acquire a nontrivial phase due to the winding of the classical solution, and (ii) a fermionic zero mode used in the literature is shown not to be normalizable.

Clash of discrete symmetries for the supersymmetric kink on a circle

We consider the

BOUNDARY TERMS IN SUPERGRAVITY AND SUPERSYMMETRY

N=1

Comment on: “One loop renormalization of soliton quantum mass corrections in (1+1)-dimensional scalar field theory models”: [Phys. Lett. B 542 (2002) 282]

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.

Comment on: “One loop renormalization of soliton quantum mass corrections in (1+1)-dimensional scalar field theory models”

We begin with the simplest possible introduction to supergravity, and then discuss its spin-3/2 stress tensor. Next, we discuss boundary conditions on fields and boundary actions for N = 1 supergravity. Finally, we discuss new boundary contributions to the mass and central charge of monopoles in N = 4 super Yang–Mills theory. All models are in (3+1) dimensions.

Analysis of User Needs for Solar Cooker Acceptance

Abstract We refute the claim that previous works on the one-loop quantum mass of solitons had incorrectly dropped a surface term from a partial integration. Rather, the paper quoted in the title contains a fallacious derivation with two compensating errors. We also remark that the φ 2 cos 2 ln( φ 2 ) model considered in that paper does not have solitons at the quantum level because at two-loop order the degeneracy of the vacua is lifted. This may be remedied, however, by a supersymmetric extension.