Domain walls are the simplest type of topological defects formed at cosmological phase transitions, and one of the most constrained. Their studies typically assume a quartic double well potential, but this model is not fully representative of the range of known or plausible particle physics models. Here, we study the cosmological evolution of domain walls in two other classes of potentials. The Sine-Gordon potential allows several types of walls, interpolating between different pairs of minima (which demands specific numerical algorithms to separately measure the relevant properties of each type). The Christ-Lee potentials parametrically interpolates between sextic and quartic behavior. We use multiple sets of simulations in two and three spatial dimensions, for various cosmological epochs and under various choices of initial conditions, to discuss the scaling properties of these networks. In the Sine-Gordon case, we identify and quantify deviations from the usual scaling behavior. In the Christ-Lee case, we discuss conditions under which walls form (or not) and quantify how these outcomes depend on parameters such as the energy difference between the false and true vacua and the expansion rate of the Universe. Various biased initial conditions are also addressed in the Appendixes. Finally, we briefly comment on the possible cosmological implications of our results.

Portugal

R. Heilemann

M.C. Rosa

Finland

J.R.C.C.C. Correia

C.J.A.P. Martins

Domain wall evolution beyond quartic potentials: The Sine-Gordon potential and Christ-Lee potentials

It has recently been pointed out that rotation in internal space can induce superradiance. We explore this effect in non-topological solitons of the two-field Friedberg-Lee-Sirlin model. This renormalizable model admits very large solitons, making the perturbative scattering equations highly sensitive to boundary conditions and requiring a relaxation method for their solution. We find that the energy extraction rate is strongly influenced by the mass hierarchy of the two scalars, and solitons with lower internal frequencies lead to more peaks in the spectra of the amplification factors. Additionally, we derive absolute bounds on the amplification factors for general ingoing modes using a linear fractional optimization algorithm and establish analytical bounds near the mass gap.

China

Guo-Dong Zhang

Cheng-Hao Li

United Kingdom

Qi-Xin Xie

Shuang-Yong Zhou

Superradiance of Friedberg-Lee-Sirlin solitons

We propose a method to numerically determine the location of a critical point in general systems using the finite-size scaling of Lee-Yang zeros. This method makes use of the fact that the ratios of Lee-Yang zeros on various spatial volumes intersect at the critical point. While the method is similar to the Binder-cumulant analysis, it is advantageous in suppressing the finite-volume effects arising from the mixing of variables in general systems. We show that the method works successfully for numerically locating the critical point in the three-dimensional three-state Potts model with a nonzero external field.

Japan

Tatsuya Wada

Masakiyo Kitazawa

Kazuyuki Kanaya

Locating Critical Points Using Ratios of Lee-Yang Zeros

We study some phenomenological aspects of Lee-Wick (LW) QED. In particular, we show that LW QED implies charge dequantization and a flavor-dependent LW scale. We study the implications of the Weak Gravity Conjecture (WGC) in LW QED and calculate the modified electric force and potential and use the former to reformulate the WGC in LW QED. We also calculate the photon self-energy and the Uehling potential in LW QED. We show that bounds on milli-charged particles from matter neutrality experiments set stringent limits on the LW scale of fermions and of the photon.

India

Fayez Abu-Ajamieh

Pratik Chattopadhyay

Marco Frasca

Phenomenological aspects of Lee-Wick QED

In this paper, the dimensional reduction is applied to the Lee-Wick electrodynamics in which the classical sources are confined on a spatial plane. As result, the Lee-Wick pseudoelectrodynamics is achieved as a nonlocal electromagnetism defined in <math><mn>1</mn><mo>+</mo><mn>2</mn></math> dimensions. The Abelian Anderson-Higgs mechanism is so introduced in the Lee-Wick pseudo-electrodynamics through a complex scalar sector in <math><mn>1</mn><mo>+</mo><mn>2</mn></math> dimensions, breaking spontaneously the <math><mi>U</mi><mo>(</mo><mn>1</mn><mo>)</mo></math>-gauge symmetry of the nonlocal theory. As consequence, the pseudo-Lee-Wick field acquires a light mass, beyond the usual heavy Lee-Wick mass, that is a natural mass parameter of the theory. After the spontaneous symmetry breaking takes place, classical features of the theory are discussed, as the pseudo-Proca-Lee-Wick electrodynamics, with the field equations and conservation laws. The introduction of Lee-Wick fermions also is proposed, in which it opens the discussion of a viable pseudo-Proca-Lee-Wick quantum electrodynamics in <math><mn>1</mn><mo>+</mo><mn>2</mn></math> dimensions. The unitarity at the tree level of the Lee-Wick pseudo-electrodynamics is discussed through the optical theorem.

Brazil

M. J. Neves

Classical features, Anderson-Higgs mechanism, and unitarity in Lee-Wick pseudo-electrodynamics

We construct spherically symmetric dyonic black holes in a generalized Maxwell-Friedberg-Lee-Sirlin type model with a complex scalar doublet and a symmetry breaking potential for the real scalar field, minimally coupled to Einstein gravity in asymptotically flat space. We analyze the properties of the hairy black holes and determine their domain of existence. Our discussion focuses mostly on the case of a long-ranged massless real scalar field. Our results indicate that in this case, depending on the coupling constants, the resonant hairy dyonic black holes may bifurcate from Reissner-Nordström black holes at maximal chemical potential, while the limiting solutions at minimal chemical potential may be related to the Penney solution.

Germany

Jutta Kunz

Belarus

Victor Loiko

JINR

Yakov Shnir

Hairy dyonic Reissner-Nordström black holes in an Einstein-Maxwell-Friedberg-Lee-Sirlin type model

In this paper, we investigate certain aspects of Lee–Wick electrodynamics near a semitransparent planar mirror. Specifically, we derive the modified propagator for the Lee–Wick gauge field in the presence of the mirror and conduct a detailed analysis of the interaction energy and the interaction force that arise between the mirror and a stationary point-like charge. We demonstrate that there are several peculiarities in this interaction compared to the results obtained for Maxwell electrodynamics. Our focus is on the divergences mitigated by the Podolsky mass term.

E. Rodrigues

F. Barone

L. Borges

A. Nogueira

Semi-transparent boundary in Lee–Wick electrodynamics

We take the Dyson–Schwinger Equation approach of QCD for the quark propagator at complex chemical potential to study the QCD phase transition. The phase transition line of the $$(2+1)$$ <math> <mrow> <mo>(</mo> <mn>2</mn> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> </math> -flavor QCD matter in the imaginary chemical potential region is computed via a simplified truncation scheme, whose curvature is found to be consistent with the one at real chemical potential. Moreover, the computation in the complex chemical potential plane allows us to determine the location of the Lee–Yang edge singularities. We show explicitly that the critical end point coincides with the Lee–Yang edge singularities on the real $$\mu _{B} $$ <math> <msub> <mi>μ</mi> <mi>B</mi> </msub> </math> axis. We also investigate the scaling behavior of the singularities and discuss the possibility of extrapolating the CEP from a certain range of chemical potential.

Zi-Yan Wan

Yi Lu

Fei Gao

Yu-xin Liu

Lee–Yang edge singularities in QCD via the Dyson–Schwinger equations

We revisit and extend Fisher’s argument for a Ginzburg-Landau description of multicritical Yang-Lee models in terms of a single boson Lagrangian with potential φ 2(iφ) n . We explicitly study the cases of n = 1, 2 by a Truncated Hamiltonian Approach based on the free massive boson perturbed by PT symmetric deformations, providing clear evidence of the spontaneous breaking of PT symmetry. For n = 1, the symmetric and the broken phases are separated by the critical point corresponding to the minimal model <math> <mi>M</mi> <mfenced> <mn>2</mn> <mn>5</mn> </mfenced> </math> $$ \mathcal{M}\left(2,5\right) $$ , while for n = 2, they are separated by a critical manifold corresponding to the minimal model <math> <mi>M</mi> <mfenced> <mn>2</mn> <mn>5</mn> </mfenced> </math> $$ \mathcal{M}\left(2,5\right) $$ with <math> <mi>M</mi> <mfenced> <mn>2</mn> <mn>7</mn> </mfenced> </math> $$ \mathcal{M}\left(2,7\right) $$ on its boundary. Our numerical analysis strongly supports our Ginzburg-Landau descriptions for multicritical Yang-Lee models.

Hungary

Máté Lencsés

Alessio Miscioscia

Italy

Giuseppe Mussardo

Gábor Takács

Ginzburg-Landau description for multicritical Yang-Lee models

The Friedberg–Lee–Sirlin (FLS) model is a well-known renormalizable theory of scalar fields that provides for the existence of non-topological solitons. Since this model was proposed, numerous works have been dedicated to studying its classical configurations and its general suitability for various physical problems in cosmology, quantum chromodynamics, etc. In this paper, we study how Q-balls in effective field theory (EFT) reproduce non-topological solitons in the full FLS theory. We obtain an analytical description of the simplified model and compare the results with numerical calculations and perturbation theory. We also study the condensation of charged bosons on the domain wall. A full numerical solution allows us to check the EFT methods for this problem. The latter analysis is based on the application of EFT methods to significantly inhomogeneous configurations. We give an interpretation of the results in terms of the shifted boson mass and the vacuum rearrangement.

Russia

Eduard Kim

Emin Nugaev

Effectively flat potential in the Friedberg–Lee–Sirlin model