Herbert Weigel -- Quantum corrections to binding energies of BPS vortices

Friday 30 Jun 2023, 13:30 → 14:30 Europe/Berlin

Nußallee 14-16/1.022 (HISKP) - Seminar Room III (HISKP)

Speaker: Herbert Weigel (Stellenbosch U.)

 

Abstract: Quantum corrections to soliton type solutions with higher baryon number in non-linear field theories have been an issue ever since the discovery of the H-dibaryon solution in the Skyrme model. This question also concerns the stability of configurations that could describe nuclei with high baryon number. In soliton models that number equals the topological charge. There have been estimates of quantum corrections but their reliability suffers from lacking renormalizability. In one space dimension renormalizability can be established but the solitons with higher topological charges are merely widely separated copies of the soliton with unit topological charge. In three space dimensions soliton stability either requires higher order derivative interactions, which are not renormalizable, or the incorporation of short range fields that make calculations beyond the classical approximation essentially 
impossible. In two space dimensions vortices with different topological charges exist in scalar electrodynamics. This is thus a role model to explore quantum energies as a function of  that charge. Especially the BPS case is interesting because then the classical energy is proportional to the charge and the quantum corrections decide on whether or not the higher charge vortices are stable. Within the on-shell renormalization scheme the energetically
favorable scenario turns out to be that in which vortices coalesce rather than to appear in isolation.

Key ingredients of the calculation of these quantum corrections are the scattering data for the quantum fluctuations interacting with a (static) potential generated by the vortex. Using the analytic properties of these data, in particular the Jost function, provides a compact formulation.