Filip Blaschke

We construct an S U ( 5 ) grand unified theory on domain walls in the five-dimensional space-time. In this setup, we introduce an adjoint scalar field and a singlet that together form a set of five domain-wall solutions, realizing a dynamical brane world. The same scalar fields also localize chiral fermion zero modes around the walls via the Jackiw-Rebbi mechanism, break S U ( 5 ) down to the Standard Model gauge group via geometric Higgs mechanism and simultaneously trap gauge fields through a field-dependent gauge kinetic term. Furthermore, they enable localization of the Higgs field, providing a novel solution to the doublet-triplet splitting problem. As a result, all essential ingredients of the model are realized by a single adjoint scalar field and a singlet, making the construction very economical. We propose two realizations of the Higgs sector, derive the four-dimensional effective theory, and demonstrate that the Standard Model Yukawa couplings at the weak scale can be reproduced from the five-dimensional Yukawa couplings by the renormalization group analysis with a suitable choice of parameters.

We present a dynamical picture of kink−anti-kink scattering in a pair of special Frankensteinian potentials made of piecewise quadratic and linear pieces. Specifically, we focus on models that support kinks without skin and core regions. We propose an intuitive interpretation for these models as being essentially free massive theories with a built-in particle-pair-like production mechanism that enters into the dynamics above certain field-value thresholds. We present results concerning the kink’s characteristics depending on these thresholds and the distribution of bouncing windows. We show that the second model exhibits a phase-transition-like property in which the nature of collisions switches from disintegration into a massive wave to the production of oscillons for large segments of initial velocities when the field threshold is low enough.

Using a renormalization-inspired perturbation expansion we show that oscillons in a generic field theory in ( 1 + 1 ) dimensions arise as dressed Q-balls of a universal (up to the leading nonlinear order) complex field theory. This theory reveals a close similarity to the integrable complex sine-Gordon model, which possesses exact multi- Q -balls. We show that excited oscillons, with characteristic modulations of their amplitude, are two-oscillons bound states generated from a two Q -ball solution.

Using renormalization group theory we show that oscillons in ( 1 + 1 ) dimensions can be obtained, at the leading nonlinear order, from Q -balls of universal complex field theories. For potentials with a nonzero cubic or quartic term the universal Q -ball theory is well approximated by the integrable complex sine-Gordon model. This allows us to generalize the usual perturbative expansion by Fodor beyond the simplest unmodulated oscillon case. Concretely, we explain the characteristic amplitude modulations of excited oscillons as an effect of formation of a two-Q-ball (two-oscillon) bound state. Published by the American Physical Society 2025