I review the standard instanton framework for determining the $\textit{θ}$-dependence of instanton-dominated correlation functions in QCD. I then contrast these well-established semiclassical results with the recent assertion of refs. [1, 2] that $\textit{θ}$-phases are absent and that strong interactions preserve CP for all values of $\textit{θ}$. In all scenarios considered, the $\textit{θ}$-dependence is shown to be intrinsically non-trivial, being governed either by instantons in the weak-coupling regime or by alternative, non-perturbative considerations when the theory is strongly coupled.

United Kingdom

Valentin Khoze

A note on instantons, $\textit{θ}$-dependence and strong CP

We consider the Carrollian conformal field theories involving scalar operators in the momentum representation. The momentum space Ward identities are explicitly solved to obtain the different branches of 2 and 3 point Carrollian conformal correlators in the momentum space. These branches are symmetry-allowed structures, characterized by different analytic structures in the Carrollian energies, and are not necessarily realized simultaneously in a single consistent theory. For specific values of the conformal dimensions, the three-point functions in momentum space exhibit logarithmic behaviour. This has no analogue in position space and instead originates from singularities in the Fourier transform relating position and momentum space correlators. We also analyze the Carrollian limit of CFT 2 and 3 point functions of scalar operators in momentum space. By taking different scalings of CFT correlators with respect to the speed of light, we obtain different branches of the Carrollian conformal correlators in the momentum space.

Italy

Raffaele Marotta

Arvind Shekar

India

Mritunjay Verma

Carrollian conformal theories in momentum space

In this work, we present a self-consistent prediction for the gravitational wave signal arising from confinement-induced phase transitions in hidden non-Abelian $\textit{SU}$ ($\textit{N}$) gauge theories with $\textit{F}$ light flavors. To do this, we impose perturbativity and unitarity constraints on the thermal effective potential to identify the portion of parameter space that admits a reliable effective field theory description. We also include the Polyakov-loop-improved finite-temperature potential for both $\textit{N}$ = 3 and $\textit{N}$ = 4, where $\textit{N}$ is the number of dark colors, using an approximate computation of the mediating effects. We compute the resulting gravitational wave spectrum and delineate the regions of parameter space that remain phenomenologically viable after imposing theoretical consistency conditions. We find that these constraints make uncovering a stochastic background gravitational wave signal in this scenario more challenging, even for proposed future detectors.

United States

Rachel Houtz

Martha Ulloa

Mia West

Gravitational waves from confining dark sectors with self-consistent effective potentials

According to the island formula, information in the code subspace defined in the black hole interior is embedded in the Hawking radiation after the Page time. At first sight, this embedding suggests that operations acting on the Hawking radiation could modify the information in the code subspace, potentially leading to an apparent violation of causality. Indeed, in previous studies based on the PSSY model, which incorporates only the topological degrees of freedom of gravity, it was shown that when the error is sufficiently large, a violation of causality can arise, as indicated by a nonvanishing mutual information.

Japan

Akihiro Miyata

Tomonori Ugajin

Black hole interior and quantum error correction with dynamical gravity

We investigate how the junction law for multipartite entanglement is realized in confining holographic backgrounds, using genuine multi-entropy (GM) as our main diagnostic. We first study an AdS hard-wall toy model as an analytic benchmark, where multi-way cuts and junction geometries can be analyzed explicitly. In this setup, we classify the relevant saddles, determine the dominant phases, and show that the genuinely multipartite contribution diagnosed by GM is localized near the junction. We also examine how this structure depends on subsystem sizes, asymmetry, and the confinement scale, including phase transitions between competing saddles. We then move beyond the hard-wall benchmark to smooth confining geometries, focusing on the D4-soliton and D3-soliton backgrounds and formulating the corresponding framework also for the Klebanov-Strassler background. In the smooth-cap examples, we find that the junction picture persists, while the detailed phase structure differs from the hard-wall case: in particular, the hard-wall plateau does not survive, and GM instead decreases monotonically and vanishes at a finite critical scale. We also find that the short-distance behavior is background-dependent, with GM ~ $\textit{L}$ in the D4-soliton background, GM ~ $\textit{L}$ in the D3-soliton background, and GM ~ $\textit{L}$ (log $\textit{L}$) in the Klebanov-Strassler background. These results clarify which features of the junction-law picture are robust in confining holography and which features of the phase structure and short-distance scaling are background-dependent.

Taiwan

Norihiro Iizuka

The junction law for multipartite entanglement in confining holographic backgrounds

We consider a general class of large $\textit{N}$ vector-like theories in $\textit{d}$ = 2 + 1 in a Hamiltonian approach. We show that by using lightcone quantization and the $\textit{N}$ → ∞ limit, we can diagonalize the Hamiltonian exactly and construct the eigenstates, spectral density, S-matrix, and form factors for the theory. For concreteness, we mainly focus on QED at large $\textit{N}$ as an explicit example. We comment on extending the approach to finite $\textit{N}$ calculations.

A. Fitzpatrick

Anastasiia Novikova

Noah Ring

Hamiltonian truncation of large $\textit{N}$ $\textit{f}$ QED and large $\textit{N}$ vector-like theories in $\textit{d}$ = 2 + 1

We apply, for the first time, Bayes Linear Emulation and History Matching to the calibration of non-perturbative models in Monte Carlo event generators. In contrast to the usual approach of “Monte Carlo tuning”, History Matching does not result in best-fit plus ellipsoidal parameter uncertainty estimates but instead identifies all parameter space regions that are consistent with data. This approach leads to a systematic and robust quantification of parametric uncertainties in the models, especially in those challenging cases where different, possibly disjoint, regions of parameter space deliver similar results, which are usually not properly treated with current methodology. We highlight the power of this method with the hadronisation models available through S : the built-in cluster fragmentation A and string fragmentation through an interface to P .

Andrew Iskauskas

Max Knobbe

Frank Krauss

Germany

Steffen Schumann

Robust calibration of non-perturbative models with history matching

We study the light asymptotic limit of the one-point torus conformal block in $\textit{A}$ Toda field theory. Through the AGT correspondence, this problem can be translated into the computation of the instanton partition function of four-dimensional $$ \mathcal{N} $$ = 2 U($\textit{n}$) supersymmetric Yang-Mills theory, which we then examine in the limit $\textit{b}$ → 0 at fixed conformal dimensions. We show that, in this regime, the instanton sum simplifies drastically: for each Young diagram, only boxes with specific arm lengths contribute to the bifundamental factors. Exploiting this property, we derive an explicit representation for the light one-point torus $\textit{W}$ conformal block valid for arbitrary $\textit{n}$ ≥ 2.

Armenia

Armen Poghosyan

Hasmik Poghosyan

The $\textit{W}$ $\textit{n}$ light one-point torus conformal block

The BM@N experiment (Baryonic Matter at the Nuclotron) is the first fixed-target experiment at the JINR NICA accelerator complex. In this work, data on the interactions of a carbon-ion beam with kinetic energies of 4.0A GeV and 4.5A GeV with C, Al, Cu, and Pb targets are used to measure transverse momentum spectra and rapidity distributions of Λ hyperon yields. The results are compared with the predictions of DCM-SMM, UrQMD, and PHSD transport models and with the Λ yield measurements in other experiments at similar collision energies.

Russia

S. Afanasiev

G. Agakishiev

A. Aleksandrov

E. Aleksandrov

I. Aleksandrov

P. Alekseev

K. Alishina

V. Astakhov

T. Aushev

V. Azorskiy

V. Babkin

N. Balashov

R. Barak

A. Baranov

D. Baranov

N. Baranova

N. Barbashina

S. Bazylev

M. Belov

D. Blau

V. Bocharnikov

G. Bogdanova

E. Bondar

E. Boos

E. Bozorov

M. Buryakov

S. Buzin

A. Chebotov

D. Chemezov

J. Chen

A. Demanov

D. Dementev

A. Dmitriev

J. Drnoyan

D. Dryablov

B. Dubinchik

Bulgaria

P. Dulov

A. Egorov

D. Egorov

V. Elsha

A. Eviev

A. Fediunin

Kazakhstan

A. Fedosimova

I. Filippov

I. Filozova

D. Finogeev

I. Gabdrakhmanov

O. Gavrischuk

K. Gertsenberger

O. Golosov

V. Golovatyuk

P. Grigoriev

M. Golubeva

F. Guber

S. Ibraimova

D. Idrisov

T. Idrissova

A. Iusupova

A. Ivashkin

A. Izvestnyy

V. Kabadzhov

Uzbekistan

A. Kakhorova

Sh. Kanokova

M. Kapishin

V. Karjavin

D. Karmanov

N. Karpushkin

R. Kattabekov

V. Kekelidze

S. Khabarov

P. Kharlamov

G. Khudaiberdyev

Yu. Kiryushin

P. Klimai

V. Kolesnikov

A. Kolozhvari

V. Kondratiev

Yu. Kopylov

M. Korolev

L. Kovachev

I. Kovalev

I. Kruglova

V. Kozlov

S. Kuklin

E. Kulish

A. Kurganov

V. Kutergina

A. Kuznetsov

E. Ladygin

D. Lanskoy

N. Lashmanov

I. Lebedev

V. Lenivenko

R. Lednický

V. Leontiev

E. Litvinenko

D. Lyapin

China

Y. Ma

A. Makankin

A. Makhnev

Production of Λ hyperons in 4.0A GeV and 4.5A GeV carbon-nucleus interactions at the Nuclotron

Yang-Mills theory in AdS with Dirichlet boundary conditions is expected to undergo a transition as the AdS radius varies, since the boundary data is incompatible with confinement in flat space. Various mechanisms have been proposed for the disappearance of the Dirichlet boundary condition. From the boundary viewpoint, the associated 3$\textit{d}$ CFT is a deformation of a generalised free theory of non-Abelian conserved currents, with the deformation governed by the bulk gauge coupling. We test these scenarios by deriving non-perturbative constraints from the numerical conformal bootstrap of the four-point function of non-Abelian conserved currents. We rule out the scenario in which the boundary current decouples. Bounds on the lightest scalar operators disfavour a bulk Higgs mechanism and instead point to a transition driven by a scalar singlet becoming marginal. We also obtain bounds on other scalar operators and on the current central charge, and we refine character-based techniques incorporating parity and charge-conjugation symmetry to determine the operator spectrum of the 3$\textit{d}$ Generalised Free Vector theory. These results may be of independent interest beyond Yang-Mills theory in AdS.