Majorana zero mode-soliton duality and in-gap and BIC bound states in modified Toda model coupled to fermion

• Published in: The journal of high energy physics Vol. 2022; no. 9; pp. 82 - 69
• Main Authors: Blas, H., Monsalve, J. J., Quicaño, R., Pereira, J. R. V.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 12-09-2022; Springer Nature B.V; SpringerOpen
• Subjects: Classical and Quantum Gravitation; Continuity (mathematics); Coupling; Elementary Particles; Fermions; Field Theories in Lower Dimensions; Field theory; High energy physics; Integrable Field Theories; Integrable Hierarchies; Localization; Mathematical models; Physics; Physics and Astronomy; Quantum computing; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; Scalars; Simulation; Solitary waves; Solitons Monopoles and Instantons; String Theory; Superconductivity; Topology; Field Theories in Lower Dimensions; Integrable Field Theories; Integrable Hierarchies; Solitons Monopoles and Instantons
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP09(2022)082

A
bstract
A two-dimensional field theory of a fermion chirally coupled to Toda field plus a scalar self-coupling potential is considered. Using techniques of integrable systems we obtain analytical zero modes, in-gap states and bound states in the continuum (BIC) for topological configurations of the scalar field. Fermion-soliton duality mappings are uncovered for the bound state spectrum, which interpolates the weak and strong coupling sectors of the model and give rise to novel Thirring-like and multi-frequency sine-Gordon models, respectively. The non-perturbative effects of the back-reaction of the fermion bound states on the kink are studied and it is shown that the zero mode would catalyze the emergence of a new kink with lower topological charge and greater slope at the center, in the strong coupling limit of the model. For special topological charges and certain relative phases of the fermion components the kinks can host Majorana zero modes. The Noether, topological and a novel nonlocal charge densities satisfy a formula of the Atiyah-Patodi-Singer-type. Our results may find applications in several branches of non-linear physics, such as confinement in QCD
2
, braneworld models, high
T
c
superconductivity and topological quantum computation. We back up our results with numerical simulations for continuous families of topological sectors.