Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2609.12709

The Jackiw-Rebbi model. Bose/Fermi one-loop Kink mass shifts

J. Mateos Guilarte
View original source ↗Read source document ↗Export metadata ↓

Abstract

Scalar and spinor Kink fluctuations are summarized in the Jackiw-Rebbi model. Canonical quantization is conventionally achieved by promoting the coefficients of the scalar and spinor field expansions to bosonic/fermionic creation/annihilation operators. One-particle states for bosons, respectively for fermions, are supplied by the scalar eigenfunctions of the Schr$\ddot{\rm o}$dinger, respectively, the eigenspinors of the Dirac Hamiltonian, evaluated either on the ground state or the Kink background. One-loop kink mass shifts are computed induced either by bosons or fermions. Both bound and scattering states contribute when the quanta are trapped by or scattered off the Kink. Zero modes of Kink fluctuations bosonic and fermionic do not modify the Kink mass at one-loop order. The Dashed-Hasslacher-Neveu prescription, derived in the canonical quantization framework, is generalized to the fermionic realm. Alternatively, quantization à la Feynman of the Jackiw-Rebbi model in the spaces of Kink scalar and spinor fluctuations is developed. It is ensured that Berezin integration over the Grassmann coefficients of the Kink spinor fluctuations leads to identical scenario as that revealed by including Fermi statistics in the DHN paradigm, at least with respect to the computation of the Kink Casimir energy.

Explore related subjects

hep-th

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

J. Mateos Guilarte. 2026-09-11. The Jackiw-Rebbi model. Bose/Fermi one-loop Kink mass shifts. https://arxiv.org/abs/2609.12709

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Six Easy Pieces: interplays among dualities in 4d, 3d and 2d

In this paper we consider 4d $\mathcal{N}=1$ $\mathrm{SU}(N)$ gauge theories with $N+1$ fundamentals, five antifundamentals and a conjugate two index antisymmetric tensor. The model has been shown to be in a mixed phase in the IR, splitting in an interacting non-Abelian Coulomb phase and a free magnetic phase. Through tensor deconfinement, we show that baryonic deformations lead to a non-Abelian free magnetic phase. Along the analysis we obtain a duality with symplectic SQCD that can be further reduced to 3d and 2d. In the 3d case the analysis of the three sphere partition function allows one to obtain dualities between $\mathrm{SU}(N)$ with a two index symmetric tensor and $\mathrm{SO}(N)$ theories. On the other hand, in 2d we recover dualities already known in the literature and propose new ones between special unitary and symplectic gauge theories.

hep-th↗
arXiv2026

Flat holography for spinor fields

We extend the hyperbolic Milne-slicing construction of flat holography in four-dimensional Minkowski spacetime from scalar fields to massless spin-$\frac{1}{2}$ fields. We solve the massive mode equation and restrict the boundary source-response analysis to the massless sector. Decomposition into harmonics on three-dimensional hyperbolic space, labeled by a continuous principal-series parameter, yields a separated-point nonlocal kernel up to the action normalization and local contact terms. The kernel has the universal form required by two-dimensional conformal covariance for spin-$\frac{1}{2}$ principal-series primaries. Then we construct regular source-normalized conformal-primary wavefunctions in planar and global coordinates on the celestial sphere $S^2$. We show that the planar source-response kernel is naturally identified with the spin-$\frac{1}{2}$ shadow transform, while inverse shadowing recovers the angular delta-function structure of the unshadowed basis. We also analyze radial renormalization by analytic continuation from the principal-series problem to a real-mass AdS$_3$ problem.

hep-th↗
arXiv2026

Off-shell recursion for all-loop planar integrands in Yang-Mills theory

In this paper, we develop in detail the off-shell recursion for planar loop integrands in Yang-Mills theory. Starting from the classical equations of motion solved with the perturbiner method, we derive an exact transfer-matrix representation of the pure-gluon sector. We then include the ghost contributions to the loop kernels based on \cite{Tao:2025fch}. Finally, as an example, we work out the two-loop recursion in detail and conclude a general recursion strategy for two-loop planar integrands whose external legs are gluons.

hep-th↗