We propose a new inverse seesaw model based on hidden local <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo></math> symmetry framework where the inverse seesaw mechanism is induced at one loop level. A Majorana mass term of singlet fermion is forbidden by the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo></math> symmetry and it is generated at one-loop level by introducing relevant particle contents to get loop diagram, inducing inverse seesaw mechanism. The same particle contents also contribute to lepton magnetic(electric) dipole moment and lepton flavor violating decays without chiral suppression. We can then obtain sizable muon anomalous magnetic dipole moment that accommodate with deviation from the standard model prediction. The constraints from lepton flavor violating decays and electron magnetic(electric) dipole moment are also discussed to explore testability of the model.

China

Takaaki Nomura

Japan

Hiroshi Okada

Radiative inverse seesaw model with hidden <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo></math> gauge symmetry enhancing lepton <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>g</mi><mo>−</mo><mn>2</mn></math>

In the heavy quarkonium decay process <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>V</mi><mo stretchy="false">→</mo><mi>g</mi><mi>g</mi><mi>g</mi></math> (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>V</mi><mo>=</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><mo>,</mo><mi mathvariant="normal">ϒ</mi></math>), making a definite prediction including relativistic corrections has so far remained a significant challenge. In this work, we study this decay process by taking into account the relativistic corrections in the Bethe-Salpeter formalism, where the relativistic bound-state wave function of quarkonium is obtained by solving the Bethe-Salpeter equation under the covariant instantaneous ansatz. Through analytical calculation, we find that some polarized decay widths vanish due to the helicity selection rule, which suppresses the corresponding helicity amplitudes. Owing to helicity flip symmetry and phase space symmetry, the nonvanishing polarized decay widths are not all independent; they are related through a set of symmetry relations. Then we obtain the unpolarized decay width formula <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Γ</mi><mo stretchy="false">(</mo><mi>V</mi><mo stretchy="false">→</mo><mi>g</mi><mi>g</mi><mi>g</mi><mo stretchy="false">)</mo><mo>=</mo><mfrac><mrow><mn>80</mn><mo stretchy="false">(</mo><msup><mi>π</mi><mn>2</mn></msup><mo stretchy="false">−</mo><mn>9</mn><mo stretchy="false">)</mo><msubsup><mi>α</mi><mi>s</mi><mn>3</mn></msubsup><msubsup><mi>N</mi><mi>V</mi><mn>2</mn></msubsup><msubsup><mi>β</mi><mi>V</mi><mn>3</mn></msubsup></mrow><mrow><mn>81</mn><msup><mi>π</mi><mrow><mn>9</mn><mo stretchy="false">/</mo><mn>2</mn></mrow></msup><mi>M</mi></mrow></mfrac><mo stretchy="false">(</mo><mn>1</mn><mo>−</mo><mi>κ</mi><mfrac><msubsup><mi>β</mi><mi>V</mi><mn>2</mn></msubsup><msup><mi>M</mi><mn>2</mn></msup></mfrac><mo stretchy="false">)</mo></math>, where the factor <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>κ</mi><mfrac><msubsup><mi>β</mi><mi>V</mi><mn>2</mn></msubsup><msup><mi>M</mi><mn>2</mn></msup></mfrac></math> arises from the relativistic corrections with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>κ</mi><mo>≡</mo><mfrac><mrow><mn>3</mn><mo stretchy="false">(</mo><mn>112</mn><mo stretchy="false">+</mo><mn>25</mn><msup><mi>π</mi><mn>2</mn></msup><mo stretchy="false">)</mo></mrow><mrow><mn>16</mn><mo stretchy="false">(</mo><msup><mi>π</mi><mn>2</mn></msup><mo stretchy="false">−</mo><mn>9</mn><mo stretchy="false">)</mo></mrow></mfrac></math>. Furthermore, including both relativistic and QCD radiative corrections within the factorization assumption, our predictions of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><mi>V</mi><mo stretchy="false">→</mo><mi>g</mi><mi>g</mi><mi>g</mi><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><mi>V</mi><mo stretchy="false">→</mo><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup><mo stretchy="false">)</mo></math> agree well with their experimental data. As a crossing check, with the experimental value of the ratio <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>R</mi><mi>V</mi></msub><mo>=</mo><mfrac><mrow><mi mathvariant="normal">Γ</mi><mo stretchy="false">(</mo><mi>V</mi><mo stretchy="false">→</mo><mi>g</mi><mi>g</mi><mi>g</mi><mo stretchy="false">)</mo></mrow><mrow><mi mathvariant="normal">Γ</mi><mo stretchy="false">(</mo><mi>V</mi><mo stretchy="false">→</mo><msup><mi>e</mi><mo stretchy="false">+</mo></msup><msup><mi>e</mi><mo stretchy="false">−</mo></msup><mo stretchy="false">)</mo></mrow></mfrac></math> and our result for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>R</mi><mi>V</mi></msub></math>, we extract <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>α</mi><mi>s</mi></msub><mo stretchy="false">(</mo><msub><mi>M</mi><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></msub><mo>/</mo><mn>2</mn><mo stretchy="false">)</mo><mo>=</mo><mn>0.31</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>α</mi><mi>s</mi></msub><mo stretchy="false">(</mo><msub><mi>M</mi><mi mathvariant="normal">ϒ</mi></msub><mo>/</mo><mn>2</mn><mo stretchy="false">)</mo><mo>=</mo><mn>0.20</mn></math>, respectively.

Hong-Mei Jiang

Chao-Jie Fan

Jun-Kang He

Cui Kong

Heavy quarkonium decay <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>V</mi><mo stretchy="false">→</mo><mi>g</mi><mi>g</mi><mi>g</mi></math> with both relativistic and QCD radiative corrections

We determine the scaling dimensions in the boundary CFT corresponding to the O($\textit{N}$) model in EAdS . The CFT data accessible to the 4-point boundary correlator of fundamental fields are extracted in $\textit{d}$ = 2 and $\textit{d}$ = 4, at a finite coupling, and to the leading nontrivial order in the 1$\textit{/N}$ expansion. We focus on the non-singlet sectors, namely the anti-symmetric and symmetric traceless irreducible representations of the O($\textit{N}$) group, extending the previous results that considered only the singlet sector. Studying the non-singlet sector requires an understanding of the crossed-channel diagram contributions to the $\textit{s}$-channel conformal block decomposition. Building upon an existing computation, we present general formulas in $\textit{d}$ = 2 and $\textit{d}$ = 4 for the contribution of a $\textit{t}$-channel conformal block to the anomalous dimensions of $\textit{s}$-channel double-twist operators, derived for external scalar operators with equal scaling dimensions. Up to some technical details, this eventually leads to the complete picture of 1$\textit{/N}$ corrections to the CFT data in the interacting theory.

Czechia

Jonáš Dujava

Petr Vaško

Finite-coupling spectrum of O($\textit{N}$) model in AdS

We present a search for solar axions produced through the axion-electron coupling ($\textit{g}$ ) using data from a novel 7-GridPix detector installed at the CERN Axion Solar Telescope (CAST). The detector, featuring ultra-thin silicon nitride windows and multiple veto systems, collected approximately 160 hours of solar tracking data between 2017–2018. Using machine learning techniques and the veto systems, we achieved a background rate of 1.06 × 10 keV cm s at a signal efficiency of about 80% in the 0.2 to 8 keV range. Analysis of the data yielded no significant excess above background, allowing us to set a new upper limit on the product of the axion-electron and axion-photon couplings of $\textit{g}$ · $\textit{g}$ < 7.35 × 10 GeV at 95% confidence level for axion masses below 10 meV. This result improves upon the previous best helioscope limit and demonstrates the potential of GridPix technology for rare event searches. Additionally, we derived a limit on the axion-photon coupling of $\textit{g}$ < 9.0 × 10 GeV at 95% CL, which, while not surpassing CAST’s best limit, provides complementary constraints on axion models.

Spain

K. Altenmüller

Greece

V. Anastassopoulos

Switzerland

S. Arguedas-Cuendis

France

S. Aune

Germany

J. Baier

K. Barth

H. Bräuninger

Italy

G. Cantatore

F. Caspers

J. Castel

Türkiye

S. Çetin

Denmark

F. Christensen

C. Cogollos

T. Dafni

M. Davenport

United States

T. Decker

K. Desch

D. Díez-Ibáñez

B. Döbrich

E. Ferrer-Ribas

H. Fischer

W. Funk

J. Galán

J. García

A. Gardikiotis

I. Giomataris

J. Golm

C. Hailey

Canada

M. Hasinoff

D. Hoffmann

I. Irastorza

J. Jacoby

A. Jakobsen

Croatia

K. Jakovčić

J. Kaminski

M. Karuza

S. Kostoglou

C. Krieger

B. Lakić

J. Laurent

G. Luzón

C. Malbrunot

C. Margalejo

M. Maroudas

South Korea

L. Miceli

H. Mirallas

P. Navarro

L. Obis

A. Özbey

K. Özbozduman

T. Papaevangelou

O. Pérez

M. Pivovaroff

Romania

M. Rosu

E. Ruiz-Chóliz

J. Ruz

T. Schiffer

S. Schmidt

M. Schumann

Y. Semertzidis

S. Solanki

L. Stewart

T. Vafeiadis

J. Vogel

K. Zioutas

Search for solar axions produced through the axion-electron coupling $\textit{g}$

We argue that $\textit{perturbatively flat vacua}$ (PFVs) introduced in $\textit{Phys. Rev. Lett.}$ (2020) 211603 are dual to M-theory compactifications on $\textit{G}$ -manifolds, enabling the enumeration of potentially novel $\textit{G}$ -manifolds via solutions to Diophantine equations in type IIB flux quanta. Independently, we show that warping corrections to the effective action of type IIB flux vacua grow parametrically at large complex structure, and we demonstrate that these corrections can nonetheless be captured by a classical geometric computation in M-theory.

Jakob Moritz

$\textit{G}$

In the context of fitting cosmological models, parameter degeneracy remains a central issue. This paper critically examines traditional methods for constraining parameters and focuses on the <italic>G</italic> factor as a tool for evaluating the quality of observational data. To ensure analytical independence, two datasets-Cosmic Chronometers (CC) and Baryon Acoustic Oscillations (BAO)-were utilized as samples for parameter fitting, supplemented by Markov Chain Monte Carlo (MCMC) simulations. The Figure of Merit (FoM) matrix served as the final criterion for assessing fitting performance. The results show that the <italic>G</italic> factor of the CC dataset increases linearly with redshift <italic>z</italic>, whereas the <italic>G</italic> factor of the BAO dataset follows a cubic relationship. Further analysis indicates that the FoM value for datasets with high <italic>G</italic> factors is significantly higher than that for datasets with low <italic>G</italic> factors, thereby validating the <italic>G</italic> factor&#8217;s effectiveness as a tool for assessing observational data quality and reducing parameter degeneracy. This suggests that the <italic>G</italic> factor may serve as a diagnostic tool and selection criterion for optimizing observational datasets in future research.

Yuan-Bo Xie

Yun-Dong Wu

Wei Hong

Tong-Jie Zhang

Exploring the cosmological model degeneracy with a new evaluate factor <italic>G</italic>

The recent observation of multiple near-threshold structures in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup></math> annihilation—including <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ψ</mi><mo stretchy="false">(</mo><mn>3770</mn><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>G</mi><mo stretchy="false">(</mo><mn>3900</mn><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>R</mi><mo stretchy="false">(</mo><mn>3760</mn><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>R</mi><mo stretchy="false">(</mo><mn>3780</mn><mo stretchy="false">)</mo></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>R</mi><mo stretchy="false">(</mo><mn>3810</mn><mo stretchy="false">)</mo></math>—reveals limitations in existing models of charmonium and exotic hadrons. In this paper, we propose a unified coupled-channel description that simultaneously incorporates all five near-threshold structures using parameters constrained by hadron spectroscopy. Our model accurately reproduces the line shapes in both <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover></math> and nonopen-charm hadron (nOCH) channels, resolves the asymmetric profile of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ψ</mi><mo stretchy="false">(</mo><mn>3770</mn><mo stretchy="false">)</mo></math>, and produces the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>G</mi><mo stretchy="false">(</mo><mn>3900</mn><mo stretchy="false">)</mo></math> bump. We identify the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>R</mi><mo stretchy="false">(</mo><mn>3780</mn><mo stretchy="false">)</mo></math> as the dominant manifestation of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ψ</mi><mo stretchy="false">(</mo><mn>3770</mn><mo stretchy="false">)</mo></math>, attribute <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>R</mi><mo stretchy="false">(</mo><mn>3760</mn><mo stretchy="false">)</mo></math> to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mo stretchy="false">→</mo><mtext>nOCH</mtext></math> rescattering and suggest that <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>R</mi><mo stretchy="false">(</mo><mn>3810</mn><mo stretchy="false">)</mo></math> arises from coupling between the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ψ</mi><mo stretchy="false">(</mo><mn>1</mn><mi>D</mi><mo stretchy="false">)</mo></math> state and the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>h</mi><mi>c</mi></msub><mi>π</mi><mi>π</mi></math> channel. The significant non-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover></math> decay of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ψ</mi><mo stretchy="false">(</mo><mn>3770</mn><mo stretchy="false">)</mo></math> is explained by its near-threshold position. This analysis provides a coherent, unquenched framework centered on a charmonium <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ψ</mi><mo stretchy="false">(</mo><mn>1</mn><mi>D</mi><mo stretchy="false">)</mo></math> core for near-threshold phenomena and offers a predictive approach extendable to bottomonium systems and future data from Belle II.

Ri-Qing Qian

Xiang Liu

Unified coupled-channel description for the five near-threshold structures <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>ψ</mi><mo stretchy="false">(</mo><mn>3770</mn><mo stretchy="false">)</mo></mrow></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>G</mi><mo stretchy="false">(</mo><mn>3900</mn><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>R</mi><mo stretchy="false">(</mo><mn>3760</mn><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>R</mi><mo stretchy="false">(</mo><mn>3780</mn><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>R</mi><mo stretchy="false">(</mo><mn>3810</mn><mo stretchy="false">)</mo></math> from <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup></math> annihilation

This study investigates compact anisotropic stellar structures using the class-1 embedding technique within the framework of modified Gauss-Bonnet gravity (i.e. <italic>f</italic>( <italic>G</italic>)). A short review of the theory is presented and the field equations are formulated by considering the well-studied model, <math altimg='si29.svg'><mrow><mi>f</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mo linebreak='goodbreak'>=</mo><mi>&#945;</mi><msup><mi>G</mi><mi>m</mi></msup></mrow></math>, where <italic>m</italic> and <italic>&#945;</italic> are positive constants. Furthermore, we utilize the Karmarkar condition to establish a connection between the metric potentials <italic>g<inf>rr</inf></italic> and <italic>g<inf>tt</inf></italic>. By adopting a specific model for one of the metric potentials, we derive the second potential through the application of the Karmarkar condition. The research focuses on determining unknown constants by matching the interior space-time of these stellar models with the exterior Schwarzschild geometry. By applying the observational data of some compact star candidates such as <math altimg='si1.svg'><mrow><mi>X</mi><mi>T</mi><mi>E</mi><mi>J</mi><mn>1739</mn><mo linebreak='goodbreak'>&#8722;</mo><mn>217</mn></mrow></math>, <math altimg='si4.svg'><mrow><mi>H</mi><mi>e</mi><mi>r</mi><mi>X</mi><mo linebreak='goodbreak'>&#8722;</mo><mn>1</mn></mrow></math>, 4 <italic>U</italic>153852, <math altimg='si2.svg'><mrow><mn>4</mn><mi>U</mi><mn>1608</mn><mo linebreak='goodbreak'>&#8722;</mo><mn>52</mn></mrow></math> and <math altimg='si3.svg'><mrow><mi>C</mi><mi>e</mi><mi>n</mi><mi>X</mi><mo linebreak='goodbreak'>&#8722;</mo><mn>3</mn></mrow></math>, the study provides a rigorous analysis of the proposed model in terms of stability and physical viability through the evolution of energy constraints, cracking constraints, adiabatic index, evolution of mass function and compactness, and the hydrostatic equilibrium of forces applied on the system and confirmed that our presented model is suitable to investigate the complex interior configuration of stellar structures.

Pakistan

Azerbaijan

M.R. Shahzad

M. Shamshad

H. Nazar

Asifa Ashraf

Saudi Arabia

Mehdi Akermi

Imed Boukhris

Modeling and stability analysis of compact objects in <italic>f</italic>( <italic>G</italic>) gravity

The Tambara-Yamagami (TY) fusion category symmetry $$ \textrm{TY}\left(\mathbbm{A},\chi, \epsilon \right) $$ describes the enhanced non-invertible self-duality symmetry of a 2-dim QFT under gauging a finite Abelian group $$ \mathbbm{A} $$ . We generalize the enhanced non-invertible symmetries by considering twisted gauging which allows stacking $$ \mathbbm{A} $$ -SPTs before and after the gauging. Such noninvertible symmetries can be obtained from invertible anyon permutation symmetries of the 3-dim SymTFT. Consider a finite group $\textit{G}$ formed by (un)twisted gaugings of $$ \mathbbm{A} $$ , a 2-dim QFT invariant under topological manipulations in $\textit{G}$ admits non-invertible $\textit{G-ality defects}$. We study the classification and the physical implication of the $\textit{G}$-ality defects using the SymTFT and the group-theoretical fusion categories, with three concrete examples. 1) Triality with $$ \mathbbm{A} $$ = $\textit{ℤ}$ × $\textit{ℤ}$ where $\textit{N}$ is coprime with 3. The classification was previously determined by Jordan and Larson where the data is similar to the TY fusion categories, and we determine the anomaly of these fusion categories. 2) $\textit{p}$-ality with $$ \mathbbm{A} $$ = $\textit{ℤ}$ × $\textit{ℤ}$ where $\textit{p}$ is an odd prime. We consider two such categories $$ {\mathcal{P}}_{\pm, m} $$ which are distinguished by different choices of the symmetry fractionalization, a new data that does not appear in the TY classification, and show that they have distinct anomaly structures and spin selection rules. 3) $\textit{S}$ -ality with $$ \mathbbm{A} $$ = $\textit{ℤ}$ × $\textit{ℤ}$ . We study their classification explicitly for $\textit{N}$ < 20 via SymTFT, and provide a group-theoretical construction for certain $\textit{N}$. We find $\textit{N}$ = 5 is the minimal $\textit{N}$ to admit an $\textit{S}$ -ality and $\textit{N}$ = 11 is the minimal $\textit{N}$ to admit a group-theoretical $\textit{S}$ -ality.

Da-Chuan Lu

Zhengdi Sun

Zipei Zhang

Exploring $\textit{G}$-ality defects in 2-dim QFTs

We have studied an <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>O</mi><mo stretchy="false">(</mo><mn>4</mn><mo stretchy="false">)</mo></math> gauged <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>O</mi><mo stretchy="false">(</mo><mn>5</mn><mo stretchy="false">)</mo></math> Skyrmion on <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi mathvariant="normal">I</mi><mspace depth="0.0ex" height="0.0ex" width="-0.2em"></mspace><mi mathvariant="normal">R</mi></mrow><mrow><mn>4</mn></mrow></msup></mrow></math>, which can be seen as a static soliton in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>4</mn><mo>+</mo><mn>1</mn></math> dimensions. This is a sequel of the known <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>O</mi><mo stretchy="false">(</mo><mi>D</mi><mo stretchy="false">)</mo></math> gauged <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>O</mi><mo stretchy="false">(</mo><mi>D</mi><mo>+</mo><mn>1</mn><mo stretchy="false">)</mo></math> Skyrmions on <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi mathvariant="normal">I</mi><mspace depth="0.0ex" height="0.0ex" width="-0.2em"></mspace><mi mathvariant="normal">R</mi></mrow><mrow><mi>D</mi></mrow></msup></mrow></math> in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><mo>=</mo><mn>2</mn></math> and in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><mo>=</mo><mn>3</mn></math>, which are likewise localized to an absolute scale and topologically stable, their energies being bounded below by the winding number. In the absence of an analytic proof of existence, some such solutions are constructed numerically. Two families of solutions are found, of which only one possesses a gauge decoupling limit. The curvatures of both of these solutions decay as <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>r</mi><mrow><mo>−</mo><mn>3</mn></mrow></msup></math>, a property they share with the Yang-Mills instantons on <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi mathvariant="normal">I</mi><mspace depth="0.0ex" height="0.0ex" width="-0.2em"></mspace><mi mathvariant="normal">R</mi></mrow><mrow><mn>4</mn></mrow></msup></mrow></math>.

Francisco Navarro-Lérida

Ireland

D.H. Tchrakian

SO(4) gauged O(5) Skyrmion on <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi mathvariant="normal">R</mi><mn>4</mn></msup></math>