<p>Axion models often face the domain wall problem, which threatens the standard big bang cosmology. The Lazarides-Shafi mechanism attempts to resolve this by identifying degenerate vacua through a continuous gauge symmetry. We formulate a topological quantum field theory to isolate the essential structure of the mechanism and analyze its generalized symmetry structure, including higher-form symmetries and higher-group. This framework yields a master formula for computing the domain wall number and clarifies the higher-form symmetry conditions required for complete vacuum identification in a model-independent way. Moreover, while a domain-wall-number-one scenario eliminates all higher-form global symmetries, the theory nevertheless exhibits a nontrivial four-group structure and realizes a symmetry-protected topological phase.</p>

Italy

Motoo Suzuki

Japan

Ryo Yokokura

Lazarides-Shafi axion models as Dijkgraaf-Witten theories

Composite axions offer a scenario where the axion emerges as a pion-like state, avoiding fine-tuning of elementary scalars and ameliorating the axion quality problem. Despite these advantages, their post-inflationary cosmology remains largely unexplored, with challenges including the domain wall problem and the presence of exotic relics. We propose two composite axion models with an effective domain wall number $\textit{N}$ = 1 and study the dilution of relics via a short period of inflation. One model is based on an SU(5) chiral gauge theory, while the other employs a “gauged” U(1) Peccei-Quinn symmetry in vector-like SU($\textit{N}$) gauge theories. We identify the viable parameter space in which axion strings re-enter the horizon before or even after the QCD transition and axion dark matter is dominantly produced from the decay of the string-wall network.

Aleksandr Azatov

Mohamed Khalil

Towards a post-inflationary composite axion model

Motivated by recent progress in the spurion analysis of non-invertible selection rules (NISRs) arising from near-group fusion algebras, we further generalize the framework to a class of NISRs obtained from $\textit{ℤ}$ orbifolding of a $\textit{ℤ}$ symmetry, denoted as $\textit{ℤ}$ /$\textit{ℤ}$ . Many structural features are carried over: for instance, our labeling scheme enables systematic tracking of all couplings when constructing composite amplitudes from simpler building blocks at arbitrary loop orders in perturbation theory. Our analysis provides a transparent understanding of both low-order and all-order zeros of couplings under radiative corrections. Furthermore, we examine the fate of low-order zeros when the fusion algebra is not faithfully realized — a situation not captured by the vanilla argument of “loop-induced groupification” — and formulate a conjecture on the related aspects of particle decoupling and effective theory. Finally, we discuss the low-order versus all-order zeros in Yukawa textures from the perspective of spurion analysis.

Ling-Xiao Xu

Spurion analysis of $\textit{ℤ}$ $\textit{M}$ /$\textit{ℤ}$ 2 non-invertible selection rules: low-order versus all-order zeros

We present a new framework of grand unification that is equipped with an axion solution to the strong CP problem without a domain wall problem when the Peccei-Quinn (PQ) symmetry is spontaneously broken after inflation. Our grand unified theory (GUT) is based on a symmetry breaking pattern, SU(10) × SU(5) → SU(5) ⊃ SU(3) × SU(2) × U(1) , where SU(5) and a special embedding of SU(5) ⊂ SU(10) are broken to a diagonal subgroup SU(5) . The model contains a vector-like pair of PQ-charged fermions that transform as (anti-)fundamental representations under SU(10), so that the domain wall number is one. However, after the GUT symmetry breaking, the number of vector-like pairs of PQ-charged colored fermions is larger than one, which seems to encounter the domain wall problem. This apparent inconsistency is resolved by small instanton effects on the axion potential which operate as a PQ-violating bias term and allow the decay of domain walls. We propose a domain-wall-free UV completion for an IR model where the domain wall number appears larger than one. The model gives a prediction for a dark matter axion window, which is different from that of the ordinary post-inflationary QCD axion with domain wall number one.

China

Shihwen Hor

Yuichiro Nakai

Junxuan Xu

Small instantons and the post-inflationary QCD axion in a special product GUT

We study radius stabilization in the Randall-Sundrum model without assuming any unnaturally large stabilizing scalar potential parameter at the boundary branes (γ) by the frequently used superpotential method. Employing a perturbative expansion in 1/γ 2 and the backreaction parameter, we obtain approximate analytical expressions for the radion mass and wavefunction. We validate them through a dedicated numerical analysis, which solves the linearized coupled scalar and metric field equations exactly. It is observed that the radion mass decreases with decreasing γ. Below a critical value of γ, the radion becomes tachyonic, suggesting destabilization of the extra dimension. We also address the issue of non-Hermiticity of the differential operator that determines the radion and Kaluza-Klein (KK) mode wavefunctions in the finite γ limit. It is accomplished by finding an explicit form of the general scalar product that re-establishes the orthogonality in the KK decomposition.

Sudhakantha Girmohanta

United States

Yaoduo Wang

Note on warped compactification. Finite brane potentials and non-Hermiticity

Ignorance of the initial condition for the axion dynamics in the early Universe has led us to consider an O(1) valued initial amplitude, and that prefers the decay constant, F  a , of the QCD axion to be an intermediate scale such as 1012 GeV in order to explain the dark matter abundance. We explore a cosmological scenario of F  a  being much larger than 1012 GeV by considering the axion and modulus dynamics during inflation to set the initial amplitude. We show that if the volume modulus (radion) of the extra-dimension is stabilized mainly by the QCD contribution to the modulus potential during inflation, the QCD axion with the string-scale decay constant obtains a mass around the inflationary Hubble parameter. This means that the axion rolls down to the θ = 0 minimum during the inflation realizing almost vanishing initial amplitude, and the inflationary quantum fluctuation can be the dominant source of the current number density of axions. We find natural parameter regions where the axion explains the cold dark matter of the Universe, while the constraint on the isocurvature perturbation is avoided. The presence of the axion miniclusters or axion stars are predicted in a wide range of parameters, including the one explains the Subaru-HCS microlensing event.

Ryuichiro Kitano

Wen Yin

Role of QCD in moduli stabilization during inflation and axion dark matter

We explore the possibility that a confining first-order phase transition of a nearly-conformal dark sector generates the reported NANOGrav signal of a stochastic gravitational wave background. The visible Standard Model (SM) sector and the dark sector are initially thermally decoupled so that their temperatures are different. The nearly conformal phase transition is described by the shallow potential of a dilaton (or a radion in the 5D holographic perspective) generated by a new dark Yang-Mills field coupled to the conformal sector. For a dark sector only gravitationally connected with the visible sector, the NANOGrav signal is explained by the phase transition without contradicting the <math><mi>Δ</mi><msub><mrow><mi>N</mi></mrow><mrow><mi>eff</mi></mrow></msub></math> constraint, together with a contribution from supermassive black hole binaries. While the dilaton and dark glueballs can be produced after the phase transition, they immediately decay into dark radiation, which can help ameliorate the Hubble tension and be tested by the future CMB-S4 experiment. Alternatively, for a dark conformal sector decaying into the visible sector after the phase transition, the <math><mi>Δ</mi><msub><mrow><mi>N</mi></mrow><mrow><mi>eff</mi></mrow></msub></math> constraint is not applied and the phase transition can solely explain the NANOGrav signal.

Kohei Fujikura

NANOGrav signal from a dark conformal phase transition

5D warped extra dimension models with multiple 3-branes can naturally realize multiple hierarchical mass scales which are ubiquitous in physics beyond the Standard Model. We discuss cosmological consequences of such multi-brane models with stabilized radions. It is confirmed that for temperatures below the scale of the IR brane at the end of the extra dimension, we recover the ordinary expansion of the Universe, with the Hubble expansion rate determined by sum of the physical energy densities on all 3-branes where they are localized. In addition, we explore the cosmology for temperatures above the scales of the intermediate and IR branes where the Universe is described by a spacetime with the 3-branes replaced by an event horizon. As the temperature of the Universe cools down, phase transitions are expected to take place, and the intermediate and IR branes come out from behind the event horizon. The Goldberger-Wise mechanism for radion stabilization has a well-known problem of having a supercooled phase transition, which typically does not get completed in time. This problem is even more severe when an intermediate brane is introduced, whose scale is well above TeV, as the corresponding Hubble rate is much larger. We circumvent the problem by employing an alternative mechanism for radion stabilization with dark Yang-Mills fields, which prevents a long supercooling epoch, but still allows the strong first order phase transitions. As a result, the phase transitions in our multi-brane Universe predict a stochastic gravitational wave background with a unique multi-peak signature, which is within the sensitivity reach of future space-based gravitational wave observers. We also show that there are N − 1 radions for an N 3-brane set-up, unlike a recent claim that there exists only one radion.

South Korea

Seung Lee

Multi-brane cosmology

We examine the possibility of building a natural non-supersymmetric model of spontaneous CP violation equipped with the Nelson-Barr (NB) mechanism to address the strong CP problem. Our approach is to utilize a doubly composite dynamics where the first confinement of the CFT occurs at the scale of spontaneous CP violation (SCPV) and the second confinement at the TeV scale. A holographic dual description of this 4D set-up via a warped extra dimension with three 3-branes provides an explicit realization of this idea. In this model, radiative corrections to the strong CP phase are well under control, and the coincidence of mass scales, which we generally encounter in NB models, is addressed. Our model also provides an explanation to the quark Yukawa hierarchies, and a solution to the gauge hierarchy problem just as in the usual Randall-Sundrum model with the Higgs being localized on the TeV brane.

CERN

A natural model of spontaneous CP violation

It is remarkable that the matter fields in the Standard Model (SM) are apparently unified into the SU(5) representations. A straightforward explanation of this fact is to embed all the SM gauge groups into a simple group containing SU(5), i.e., the grand unified theory (GUT). Recently, however, a new framework “fake GUT” has been proposed. In this new framework, the apparent matter unification can be explained by a chiral gauge group G, G ⊃ SU(5). We emphasize that the SM matter fields are not necessarily embed- ded into the chiral representations to explain the apparent unification. In this paper, we discuss details of concrete realizations of the fake GUT model. We first study the model based on SU(5) × U(2) H , where SU(3) c  in the SM is from SU(5) while SU(2) L  × U(1) Y  are from the diagonal subgroups of SU(5) × U(2) H . We also extend this model to the one based on a semi-simple group, SU(5) × SU(3) H , so that U(2) H  is embedded in SU(3) H . We also show that this framework predicts rather different decay patterns of the proton, compared to the conventional GUT.