Fermionic vacuum energy from a Nielsen-Olesen vortex

Abstract

We calculate the vacuum energy of a spinor field in the background of a Nielsen-Olesen vortex. We use the method of representing the vacuum energy in terms of the Jost function on the imaginary momentum axis. Renormalization is carried out using the heat kernel expansion and zeta functional regularization. With this method well convergent sums and integrals emerge which allow for an efficient numerical calculation of the vacuum energy in the given case where the background is not known analytically but only numerically. The vacuum energy is calculated for several choices of the parameters and it turns out to give small corrections to the classical energy.

Quantum corrections to the mass of the supersymmetric vortex

“…Some concluding remarks are given in sec. 6. Technical details of the calculations related to the boundary supersymmetries are presented in the Appendix.…”

One-loop fermionic corrections to the instanton transition in the two dimensional chiral Higgs model

“…As can be seen in (13), considering only one family of fermions leads to the creation of one single fermion. This process seems to be possible in two dimensions, although it is forbidden in four dimensions because of the Witten anomaly [25].…”

“…This is checked in Fig. 2 9 The accuracy can be checked by calculating the instanton number (13) or the action of the instanton for m 2 H =m 2 W 1 that is known to be v 2 [15]. The results of the numerical integration agree to 13 decimals with the action in the latter case and at least 7 for the instanton number in any case (see Fig.…”

Quantum stabilization of a closed Nielsen-Olesen string

“…The most imperative question regarding the dynamics of a cosmic string is its stability. Studies of this question have mainly focused on infinitely long and axially symmetric string configurations [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]. Unless these configurations carry (topological) charges, as is the case, for example, for the Abelian Nielsen-Olesen string [6], they are classically unstable but can eventually be stabilized by quantum effects.…”