Abstract

We introduce a novel point-particle effective description of ANO vortex solitons in the critical Abelian Higgs Model (AHM) in d = 2 + 1 based on the small winding expansion. Identifying the effective vortices with the elementary quanta of a complex scalar field, relativistic vortex-vortex scattering amplitudes are calculated as a diagrammatic, perturbative expansion in the winding number N. Making use of powerful techniques recently developed for analyzing the post-Minkowskian two-body problem in general relativity, we efficiently extract the contribution to the loop integrals from the classical potential region, with the resulting velocity expansion subsequently resummed to all orders. The main result of this paper is an analytic expression for the classical, vortex-vortex potential at O(N2), or one-loop, with exact velocity dependence. By truncating the resulting effective Hamiltonian at O(p2) we derive an analytic, perturbative expression for the metric on the 2-vortex moduli space. Finally, the emergence of the critical AHM from the classical limit of the N = 2 supersymmetric AHM, and the resulting constraints on the point-particle EFT is described in detail using an on-shell superspace construction for BPS states in d = 2 + 1.

Details

Title
Classical dynamics of vortex solitons from perturbative scattering amplitudes
Author
Jones, Callum R. T. 1   VIAFID ORCID Logo 

 University of California Los Angeles, Mani L. Bhaumik Institute for Theoretical Physics, Department of Physics and Astronomy, Los Angeles, USA (GRID:grid.19006.3e) (ISNI:0000 0001 2167 8097) 
Pages
92
Publication year
2023
Publication date
Nov 2023
Publisher
Springer Nature B.V.
e-ISSN
10298479
Source type
Scholarly Journal
Language of publication
English
ProQuest document ID
2891042248
Copyright
© The Author(s) 2023. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.