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

Italy

Motoo Suzuki

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

Japan

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.

Masahiro Ibe

Satoshi Shirai

Keiichi Watanabe

Tsutomu Yanagida

More on fake GUT

We explore a new framework that furnishes a mechanism to simultaneously address the electroweak naturalness problem and the axion high quality problem. The framework is based on a doubly composite dynamics where the second confinement takes place after the CFT encounters the first confinement and the theory flows into another conformal fixed point. For a calculable example, we present a holographic dual description of the 4D model via a warped extra dimension model with three 3-branes. While the hierarchy problem is taken cared of by the localization of the Higgs fields on the TeV brane just as in the original Randall-Sundrum model, the Peccei-Quinn (PQ) symmetry is realized as a gauge symmetry in the bulk of the extra dimension to solve the axion quality problem. We introduce a 5D scalar field whose potential at the intermediate brane drives spontaneous breaking of the PQ symmetry. Then, the PQ breaking scale is given by the scale of the intermediate brane and is naturally small compared to the Planck scale. The axion bulk profile is significantly suppressed around the UV brane, which protects the axion from gravitational violations of the PQ symmetry on the UV brane. Our model genuinely predicts the existence of the Kaluza-Klein excitations of the QCD axion at around the TeV scale and relatively light extra Higgs bosons.

High quality axion via a doubly composite dynamics

Theories beyond the Standard Model often contain mass scales hierarchically different from the electroweak scale and the Planck scale. It has been shown that such hierarchical mass scales can be realized as typical energy scales of multiple 3-branes in a 5D warped spacetime. We present a mechanism for stabilizing the intervals between the multiple 3-branes in the warped extra dimension, by introducing a single 5D scalar field with brane-localized potentials. We discuss the radion stabilization by solving the Einstein equation and the scalar field equation of motion so that a backreaction effect on the geometry due to the presence of the scalar field is taken into account. Perturbations from the background configuration are then considered with proper identification of multiple radion degrees of freedom. By solving their equations of motion, we compute the mass spectrum of the radion-scalar field system and the radion couplings to brane-localized matter fields, which are found to be suppressed by typical energy scales and radion profiles at the branes. We also compute the mass spectrum of Kaluza-Klein gravitons and their profiles in the extra dimension. Some applications of the setup are briefly described. Our analysis provides a solid ground to build 5D warped extra dimension models with multiple 3-branes.

Multiple hierarchies from a warped extra dimension

We discuss how the topological defects in the dark sector affect the Standard Model sector when the dark photon has a kinetic mixing with the QED photon. In particular, we consider the dark photon appearing in the successive gauge symmetry breaking, SU(2) → U(1) → ℤ 2, where the remaining ℤ 2 is the center of SU(2). In this model, the monopole is trapped into the cosmic strings and forms the so-called bead solution. As we will discuss, the dark cosmic string induces the QED magnetic flux inside the dark string through the kinetic mixing. The dark monopole, on the other hand, does not induce the QED magnetic flux in the U(1) symmetric phase, even in the presence of the kinetic mixing. Finally, we show that the dark bead solution induces a spherically symmetric QED magnetic flux through the kinetic mixing. The induced flux looks like the QED magnetic monopole viewed from a distance, although QED satisfies the Bianchi identity everywhere, which we call a pseudo magnetic monopole.