Topology plays a central role in classifying solitonic configurations in field theories, providing robustness and a nonperturbative label, the so-called topological charge <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Q</mi></math>. In soliton-fermion coupled systems, the relation between the topological charge and the number of zero modes is well established through the index theorem. However, the physical consequences of the sign of the topological charge have remained largely unexplored. In this work, we study fermions in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>2</mn><mo>+</mo><mn>1</mn></math> dimensions coupled to skyrmions with target space <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="double-struck">C</mi><msup><mi mathvariant="normal">P</mi><mi>N</mi></msup></math>, particularly focusing on the backreactions of the fermions and on the sign of the topological charge. We obtain the solutions in a self-consistent manner, which exhibit an asymmetry with respect to the topological charge <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>±</mo><mi>Q</mi></math> especially in the strong coupling regimes. This asymmetry is caused by the fermionic eigenvalue problem inherent in the self-consistent formulation. Although the Lagrangian is symmetric under <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Q</mi><mo stretchy="false">→</mo><mo>−</mo><mi>Q</mi></math>, the coupled equations for the skyrmions and anti-skyrmions become inequivalent once fermionic backreaction is taken into account. We demonstrate the mechanism in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="double-struck">C</mi><msup><mi mathvariant="normal">P</mi><mn>1</mn></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="double-struck">C</mi><msup><mi mathvariant="normal">P</mi><mn>2</mn></msup></math> skyrmions, but the analysis is directly extendable for the general <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="double-struck">C</mi><msup><mi mathvariant="normal">P</mi><mi>N</mi></msup></math>.

Japan

Yuki Amari

Nobuyuki Sawado

Shintaro Yamamoto

Topological charge asymmetry in a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="double-struck">C</mi><msup><mi mathvariant="normal">P</mi><mi>N</mi></msup></math> skyrmion-fermion coupled system

We extend the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>κ</mi></math>-symmetry analysis of supersymmetric D-brane probes in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>AdS</mi><mn>2</mn></msub><mo>×</mo><msup><mi mathvariant="bold">S</mi><mn>2</mn></msup></math> attractor geometry, originally performed by Simons, Strominger, Thompson, and Yin to also include stationary—but nonstatic—worldlines carrying angular momentum along the 2-sphere. We demonstrate that certain special trajectories, with fixed radius and orbital velocity, solve the equations of motion and moreover satisfy a supersymmetry preserving condition, thus defining new <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mfrac><mn>1</mn><mn>2</mn></mfrac></math>-BPS configurations. Furthermore, these classical paths are shown to saturate a lower bound for the Hamiltonian generating global time translations, with the corresponding minimal energy depending on a generalized angular momentum vector <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="bold-italic">J</mi></mrow></math>. The direction of the latter, in turn, determines exactly which supercharges remain unbroken. Our results reveal a richer spectrum of (multiparticle) supersymmetric states in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>AdS</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>×</mo><msup><mrow><mi mathvariant="bold">S</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></math>, which can be organized into distinct selection sectors labeled by the conserved <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mn>2</mn><mo stretchy="false">)</mo></math> charges. This construction has direct applications in black hole microstate counting, the analysis of probe dynamics, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>AdS</mi><mn>2</mn></msub><mo>/</mo><msub><mi>CFT</mi><mn>1</mn></msub></math> holography.

United States

Alberto Castellano

Germany

Carmine Montella

Matteo Zatti

Supersymmetric D-brane probes in 4D <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">N</mi><mo>=</mo><mn>2</mn></math> <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>AdS</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>×</mo><msup><mrow><mi mathvariant="normal">S</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></math> attractors

Since 2019, the Extreme Energy Events (EEE) Project has installed three muon detection stations at the Svalbard Islands ( $$78.9^{\circ } \hbox {N}$$ latitude), employing scintillator-based detectors. This initiative represents the first systematic effort to monitor cosmic-muons rates at high geomagnetic latitudes beyond the Arctic Circle, with the objective of improving our understanding of cosmic-ray propagation and modulation in polar regions. The present study analyses temporal variations in the muon detection rates over a six-year period (2019–2025), including the study of periodic modulations and underlying trends in the observed rates.

Italy

M. Abbrescia

C. Avanzini

L. Baldini

R. Baldini Ferroli

G. Batignani

M. Battaglieri

E. Bossini

F. Carnesecchi

D. Cavazza

C. Cicalò

L. Cifarelli

F. Coccetti

E. Coccia

A. Corvaglia

A. Caro

D. Gruttola

S. Pasquale

L. Galante

M. Garbini

L. Ghezzer

I. Gnesi

F. Gramegna

Norway

E. Gramstad

S. Grazzi

E. Haland

Switzerland

D. Hatzifotiadou

P. Rocca

R. Liotino

G. Mandaglio

A. Margotti

G. Maron

M. Mazziotta

A. Mulliri

R. Nania

F. Noferini

F. Nozzoli

F. Ould-Saada

F. Palmonari

M. Panareo

M. Panetta

R. Paoletti

C. Pellegrino

L. Perasso

O. Pinazza

C. Pinto

S. Pisano

K. Piscicchia

L. Quaglia

M. Rasà

F. Riggi

G. Righini

C. Ripoli

M. Rizzi

B. Sabiu

G. Sartorelli

E. Scapparone

M. Schioppa

G. Scioli

A. Scribano

M. Selvi

A. Shtimermann

M. Taiuti

A. Trifirò

M. Trimarchi

C. Vistoli

L. Votano

M. Williams

A. Zichichi

R. Zuyeuski

Measurement of the cosmic-ray rate over the period 2019–2025 at very high latitude (78.9°N)

The $$ {\mathbbm{CP}}^{N-1} $$ model is an analytically tractable 2$\textit{d}$ quantum field theory which shares several properties with 4$\textit{d}$ Yang-Mills theory. By virtue of its classical integrability, this model also admits a family of integrable higher-spin auxiliary field deformations, including the $$ T\overline{T} $$ deformation as a special case. We study the $$ {\mathbbm{CP}}^{N-1} $$ model and its deformations from a geometrical perspective, constructing their soliton surfaces and recasting physical properties of these theories as statements about surface geometry. We examine how the $$ T\overline{T} $$ flow affects the unit constraint in the $$ {\mathbbm{CP}}^{N-1} $$ model and prove that any solution of this theory with vanishing energy-momentum tensor remains a solution under analytic stress tensor deformations — an argument that extends to generic dimensions and instanton-like solutions in stress tensor flows including the non-analytic, 2$\textit{d}$, root- $$ T\overline{T} $$ case and classes of higher-spin, Smirnov-Zamolodchikov-type, deformations. Finally, we give two geometric interpretations for general $$ T\overline{T} $$ -like deformations of symmetric space sigma models, showing that such flows can be viewed as coupling the undeformed theory to a unit-determinant field-dependent metric, or using a particular choice of moving frame on the soliton surface.

Christian Ferko

Australia

Michele Galli

Zejun Huang

Gabriele Tartaglino-Mazzucchelli

Soliton surfaces and the geometry of integrable deformations of the $$ {\mathbbm{CP}}^{N-1} $$ model

It was recently established that the paradigmatic Gross-Neveu model with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math> copies of two-dimensional Dirac fermions features an <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>SO</mi><mo stretchy="false">(</mo><mn>2</mn><mi>N</mi><mo stretchy="false">)</mo></math> symmetry if certain interactions are suppressed. This becomes evident when the theory is rewritten in terms of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>2</mn><mi>N</mi></math> copies of two-dimensional Majorana fermions. Mean-field theory for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>SO</mi><mo stretchy="false">(</mo><mn>2</mn><mi>N</mi><mo stretchy="false">)</mo></math> model predicts, besides the chiral Ising transition at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>g</mi><mrow><mi>c</mi><mn>1</mn></mrow></msub></math>, a second critical point <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>g</mi><mrow><mi>c</mi><mn>2</mn></mrow></msub></math> where <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>SO</mi><mo stretchy="false">(</mo><mn>2</mn><mi>N</mi><mo stretchy="false">)</mo></math> is broken down to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>SO</mi><mo stretchy="false">(</mo><mi>N</mi><mo stretchy="false">)</mo><mo>×</mo><mi>SO</mi><mo stretchy="false">(</mo><mi>N</mi><mo stretchy="false">)</mo></math>. A subsequent Wilsonian renormalization group analysis directly in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>d</mi><mo>=</mo><mn>3</mn></math> supports its existence in a generalized theory, where <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>f</mi></msub></math> copies of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>4</mn><mi>N</mi></math>-component Majorana fermions are introduced. This allows us to track the evolution of a (i) quantum anomalous Hall Gross-Neveu-Ising, (ii) symmetric-tensor, and (iii) adjoint-nematic fixed point separately. However, it turns out that (ii) and (iii) lose their criticality when approaching <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>f</mi></msub><mo>=</mo><mn>1</mn></math>, suggesting that the transition is first order. In this work, we approach the problem from the lower-critical dimension of two. We construct a Fierz-complete renormalizable Lagrangian, compute the leading order <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>β</mi></math> functions, fermion anomalous dimension, as well as the order parameter anomalous dimensions, and resolve the three universality classes corresponding to (i)–(iii). Before becoming equal to the Gaussian fixed point at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>f</mi></msub><mo>=</mo><mn>1</mn></math>, (ii) remains critical for all values of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>N</mi></mrow><mrow><mi>f</mi></mrow></msub><mo>&gt;</mo><msubsup><mrow><mi>N</mi></mrow><mrow><mi>f</mi><mo>,</mo><mi>c</mi></mrow><mrow><mi>ST</mi></mrow></msubsup><mo stretchy="false">(</mo><mi>N</mi><mo stretchy="false">)</mo><mo>≈</mo><mn>0.56</mn><mo>+</mo><mn>1.48</mn><mi>N</mi><mo>+</mo><mi mathvariant="script">O</mi><mo stretchy="false">(</mo><mi>ε</mi><mo stretchy="false">)</mo></mrow></math>, which compares well with the estimate of previous studies. We further find that (iii) becomes equal to (i) when approaching <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>f</mi></msub><mo>=</mo><mn>1</mn></math>. An instability is, however, only present in the susceptibility corresponding to the Gross-Neveu-Ising order parameter.

Bilal Hawashin

Max Uetrecht

Spontaneous symmetry breaking of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>SO</mi><mo stretchy="false">(</mo><mn>2</mn><mi>N</mi><mo stretchy="false">)</mo></mrow></math> in Gross-Neveu theory from <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>2</mn><mo>+</mo><mi>ε</mi></math> expansion

We derive decomposition formulas for supercharacters of quantum affine orthosymplectic superalgebras and twisted quantum affine superalgebras into supercharacters of their finite-type quantum sub-superalgebras, by employing Cauchy-type identities for supersymmetric Schur functions. These formulas are obtained via a folding (reduction) procedure applied to the supercharacters of the finite-dimensional general linear Lie superalgebra <math altimg='si5.svg'><mrow><mi mathvariant='fraktur'>gl</mi><mo>(</mo><mi>M</mi><mo>|</mo><mi>N</mi><mo>)</mo></mrow></math>. As a special case, our results provide explicit character formulas for a class of Kirillov-Reshetikhin modules of quantum affine algebras (and their Yangian counterparts), thereby proving a previously proposed conjecture derived from Bethe ansatz analysis.

Zengo Tsuboi

Character formulas for Kirillov-Reshetikhin modules via folding of supercharacters of <math altimg='si5.svg'><mrow><mi mathvariant='fraktur'>gl</mi><mo>(</mo><mi>M</mi><mo>|</mo><mi>N</mi><mo>)</mo></mrow></math>

In the present work, we propose to investigate the production of $$d_{N \Omega }$$ in the $$\Omega ^{-} d \rightarrow p d_{N \Omega }^-$$ process by utilizing an effective Lagrangian approach, where $$d_{N \Omega }$$ is identified as $$N\Omega $$ bound state with the binding energy $$E_{b}=2.46$$ MeV. Experimentally, the J-PARC hadron facility proposed to investigate the $$K^{-}p \rightarrow \Omega ^{-} \bar{K}^{(*)0} K^{+}$$ process, which is expected to yield an $$\Omega $$ beam with the momentum of approximately 3 GeV. Additionally, theoretical studies of the $$\psi (2S) \rightarrow \Omega ^{-} \bar{\Omega }^{+}$$ process at BESIII provided an $$\Omega $$ beam with the momentum of 774 MeV. Considering these two potential $$\Omega $$ beam sources, our estimations show that for the $$\Omega ^{-} d \rightarrow p d_{N \Omega }^-$$ process, the cross sections are $$\Big (329.7^{+26.9}_{-49.6}\Big )$$ $$\mu $$ b, $$\Big (174.0^{+26.5}_{-38.2}\Big )$$ $$\mu $$ b, $$\Big (16.9^{+7.4}_{-7.7}\Big )$$ $$\mu $$ b, and $$\Big (2.0^{+1.8}_{-1.4}\Big )$$ $$\mu $$ b at $$P_{\Omega } =$$ 0.7, 0.9, 2.0, and 4.0 GeV, respectively, where the central values are estimated with $$\Lambda _{r}=1.0$$ GeV, and the errors come from the variation of $$\Lambda _{r}$$ from 0.8 to 1.2 GeV. We also estimate the differential cross sections, which reach the maximum at the forward angle limit. In addition, since the $$d_{N \Omega }$$ dibaryon predominantly decays into $$\Xi \Lambda $$ . Therefore, we further investigate the $$\Omega ^{-} d \rightarrow p \Xi ^- \Lambda $$ process and estimate the relevant cross sections. It is expected that the present estimations can be tested by further experimental measurements at J-PARC and STCF in the future.

China

Quan-Yun Guo

Jing Liu

Dian-Yong Chen

$$d_{N \Omega }$$ production in $$\Omega d$$ scattering process

We study fully BPS and a broad class of half-BPS stationary configurations of four-dimensional Euclidean $$ \mathcal{N}=2 $$ supergravity with higher-derivative interactions. Working within the off-shell conformal supergravity framework of de Wit and Reys (arXiv:1706.04973), we analyse the complete set of Killing spinor equations and obtain the corresponding algebraic and differential constraints. We further derive the Euclidean attractor equations and evaluate the Wald entropy for the fully BPS AdS × $\textit{S}$ background. For half-BPS stationary configurations, we obtain the generalized stabilization equations expressing all fields in terms of harmonic functions on three-dimensional flat base space, extending the Lorentzian analysis of Cardoso et al. ( ) to the Euclidean signature. Our results provide a framework for studying supersymmetric saddles and computing the gravitational indices entirely within Euclidean higher-derivative supergravity, without recourse to analytic continuation.

South Korea

Soumya Adhikari

India

Abhinava Bhattacharjee

Amitabh Virmani

BPS solutions of 4d Euclidean $$ \mathcal{N}=2 $$ supergravity with higher derivative interactions

In the present paper we consider the usage of classical dynamical non-skew-symmetric <italic>r</italic>-matrices with spectral parameters in the theory of integrable systems. We construct &#8212; in complete analogy with non-dynamical case [26, 27] &#8212; general position Lax matrices satisfying classical <italic>r</italic>-matrix Poisson brackets. We consider an example of the Lie algebra <italic>gl</italic>( <italic>n</italic>), dynamical <italic>r</italic>-matrix of Calogero model (equivalent to that of [8]) and many-poled Lax matrix with <italic>N</italic> first order poles. With its help we obtain a new variant of <italic>gl</italic>( <italic>n</italic>) multi-spin-Calogero (Gaudin-Calogero) model, integrable without an additional reduction. The <math altimg='si1.svg'><mrow><mi>N</mi><mo linebreak='goodbreak'>=</mo><mn>1</mn></mrow></math> spin-Calogero case is considered in details.

Ukraine

T. Skrypnyk

On classical dynamical <italic>r</italic>-matrices, Lax algebras and integrable <italic>gl</italic>( <italic>n</italic>) spin-Calogero models

$$ \mathcal{N} $$ = 1 superconformal minimal models are the first series of unitary conformal field theories (CFTs) extending beyond Virasoro algebra. Using coset constructions, we characterize CFTs in $$ \mathcal{N} $$ = 1 superconformal minimal models using combinations of a parafermion theory, an Ising theory and a free boson theory. Supercurrent operators in the original theory also becomes sums of operators from each constituent theory. If we take our $$ \mathcal{N} $$ = 1 superconformal theories as the neutral part of the edge theory of a fractional quantum Hall state, we present a systematic way of calculating its ground state wavefunction using free field methods. Each ground state wavefunction is known previously as a sum of polynomials with distinct clustering behaviours. Based on our decomposition, we find explicit expressions for each summand polynomial. A brief generalization to $\textit{S}$ minimal models using coset construction is also included.

Yichen Hu

United Kingdom

Sirui Ning

Yehao Zhou

Decomposition of $$ \mathcal{N} $$ = 1 superconformal minimal models and their fractional quantum Hall wavefunctions