Alberto Alonso-Izquierdo, Juan Mateos Guilarte
In this paper quantum effects are investigated in a very special two-scalar field model having a moduli space of BPS domain walls, all of them sharing the same tension at the classical level. The heat kernel/zeta function regularization method will be used to control the divergences induced by the quantum wall fluctuations. A generalization of the Gilkey-DeWitt-Avramidi heat kernel expansion will be developed in order to accommodate the infrared divergences due to zero modes in the spectra of the second-order domain wall fluctuation operators, which are $N\times N$ matrix differential operators. Use of these tools in the spectral zeta function associated with the Hessian operators paves the way to obtain a general formula for the one-loop domain wall tension shifts in any (3+1)-dimensional $N$-component scalar field theory model. Application of this formula to the BPS walls of the N=2 model mentioned above reveals the breaking of the classical tension degeneracy at the quantum level. Because the main parameter distinguishing each member in the BPS domain wall moduli space is essentially the distance between the centers of two basic walls, the breaking of the degeneracy amounts to the surge in quantum-induced forces between the two constituent topological defects. In fact, depending on the value of the coupling constant and the relative distance, the wall quantum fluctuations give rise to attractive or repulsive forces between the two constituent domain walls, a phenomenon similar to that occurring between magnetic flux lines in the phase transition from Type I to Type II superconductors.
View original:
http://arxiv.org/abs/1307.0740
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