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.

United States

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

<p>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.</p>

Germany

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

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

$$ \mathcal{N} $$ = 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

Japan

Yehao Zhou

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

<p>We continue to explore the previously suggested dual regime of Yang-Baxter (YB) deformed <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">O</mi><mo stretchy="false">(</mo><mn>2</mn><mi>N</mi><mo stretchy="false">)</mo></math> sigma models, which is a new one-parametric deformation of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">O</mi><mo stretchy="false">(</mo><mn>2</mn><mi>N</mi><mo stretchy="false">)</mo></math> model. It can be obtained from the conventional YB deformed <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">O</mi><mo stretchy="false">(</mo><mn>2</mn><mi>N</mi><mo>+</mo><mn>2</mn><mo stretchy="false">)</mo></math> sigma model by freezing two isometries. The scattering matrix in the nondeformed <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">O</mi><mo stretchy="false">(</mo><mi>n</mi><mo stretchy="false">)</mo></math> model is known to coincide with the rational <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mrow><mi mathvariant="fraktur">so</mi></mrow><mi>n</mi></msub></math>-invariant <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>R</mi></math>-matrix. For <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>n</mi><mo>=</mo><mn>2</mn><mi>N</mi></math> this rational solution allows for two trigonometric deformations: the usual <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>D</mi><mi>N</mi><mrow><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo></mrow></msubsup></math> and the twisted <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>D</mi><mi>N</mi><mrow><mo stretchy="false">(</mo><mn>2</mn><mo stretchy="false">)</mo></mrow></msubsup></math>. The usual one is known to coincide with the scattering matrix of the conventional YB-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">O</mi><mo stretchy="false">(</mo><mn>2</mn><mi>N</mi><mo stretchy="false">)</mo></math> model. A natural question to ask is what sigma model corresponds to the twisted solution. In this work we claim that it is precisely our dual regime of YB-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">O</mi><mo stretchy="false">(</mo><mn>2</mn><mi>N</mi><mo stretchy="false">)</mo></math>. We find the corresponding unitarizing function <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>F</mi><mi>N</mi></msub><mo stretchy="false">(</mo><mi>θ</mi><mo stretchy="false">)</mo></math> explicitly, and, as a bonus, extract some physical properties of this system using the thermodynamic Bethe ansatz technique.</p>

Russia

Alexey Bychkov

Boris Nekrasov

Scattering in the dual regime of Yang-Baxter deformed <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="normal">O</mi><mo stretchy="false">(</mo><mn>2</mn><mi>N</mi><mo stretchy="false">)</mo></mrow></math> sigma models

It is believed that the theory of quantum gravity describing our universe is unitary. Nonetheless, if we only have access to a subsystem, its dynamics is described by nonequilibrium physics. Motivated by this, we investigate the planar limit of large $\textit{N}$ ungauged one-matrix quantum mechanics obeying the Lindblad master equation with dissipative jump terms, focusing on the existence, uniqueness, and properties of steady states that signal nonequilibrium phase transitions. In the first class of examples, where potentials are unbounded from below, we study nonequilibrium critical points above which strong dissipation allows for the existence of normalizable steady states that would otherwise not exist. In the second class of examples, termed matrix quantum optics, we find evidence of nonequilibrium phase transitions analogous to those recently reported in the quantum optics literature for driven-dissipative Kerr resonators. Preliminary results on two-matrix quantum mechanics are also presented. We implement bootstrap methods to obtain concrete and rigorous results for the nonequilibrium steady states of matrix quantum mechanics in the planar limit.

Minjae Cho

Nonequilibrium phase transitions in Large $\textit{N}$ matrix quantum mechanics

First information on the timelike electromagnetic structure of baryons in the second resonance region has been obtained from measurements of the dielectron (e <math altimg='si2.svg'><msup><mrow /><mo>+</mo></msup></math>e <math altimg='si3.svg'><msup><mrow /><mo>&#8722;</mo></msup></math>) invariant mass and angular distributions with the High Acceptance Di-Electron Spectrometer (HADES) at GSI, using a secondary pion beam impinging on CH <inf>2</inf> and C targets. The quasi-free reaction <math altimg='si1.svg'><msup><mi>&#960;</mi><mo>&#8722;</mo></msup></math>+ p &#8239;&#8594;&#8239; n e <math altimg='si2.svg'><msup><mrow /><mo>+</mo></msup></math>e <math altimg='si3.svg'><msup><mrow /><mo>&#8722;</mo></msup></math> at <math altimg='si12.svg'><msqrt><msub><mi>s</mi><mrow><mi>&#960;</mi><mi mathvariant='normal'>p</mi></mrow></msub></msqrt></math> = 1.49&#8239;GeV is isolated in several analysis steps. The data set provides a crucial test for the description of baryon timelike transitions. Close to the kinematical limit the meassured e <math altimg='si2.svg'><msup><mrow /><mo>+</mo></msup></math>e <math altimg='si3.svg'><msup><mrow /><mo>&#8722;</mo></msup></math> mass distribution shows deviations by up to a factor 8 from the Dalitz decay of a point-like baryon. Various theoretical approaches connecting information from hadronic and electromagnetic channels in the spacelike and timelike regime compare well with the measured e <math altimg='si2.svg'><msup><mrow /><mo>+</mo></msup></math>e <math altimg='si3.svg'><msup><mrow /><mo>&#8722;</mo></msup></math> invariant mass distribution, including (i) a Vector Meson Dominance amplitude containing direct photon and vector meson ( <italic>&#961;</italic>) couplings to the baryon, (ii) electromagnetic timelike baryon transition form factors in a covariant spectator-quark model, where meson cloud effects dominate, and (iii) application of dispersion theory, which demonstrates the importance of the pion electromagnetic form factors.

France

R. Abou Yassine

J. Adamczewski-Musch

O. Arnold

E.T. Atomssa

M. Becker

C. Behnke

J.C. Berger-Chen

Portugal

A. Blanco

C. Blume

M. Böhmer

Czechia

L. Chlad

Poland

I. Ciepał

S. Deb

C. Deveaux

D. Dittert

J. Dreyer

E. Epple

L. Fabbietti

J. Förtsch

P. Fonte

C. Franco

J. Friese

I. Fröhlich

T. Galatyuk

Spain

J.A. Garzón

R. Gernhäuser

R. Greifenhagen

M. Grunwald

M. Gumberidze

S. Harabasz

T. Heinz

T. Hennino

C. Höhne

F. Hojeij

R. Holzmann

M. Idzik

B. Kämpfer

K-H Kampert

B. Kardan

V. Kedych

S. Kim

I. Koenig

W. Koenig

M. Kohls

J. Kolas

B.W. Kolb

G. Korcyl

G. Kornakov

R. Kotte

W. Krueger

A. Kugler

T. Kunz

R. Lalik

K. Lapidus

S. Linev

F. Linz

L. Lopes

M. Lorenz

T. Mahmoud

L. Maier

A. Malige

J. Markert

S. Maurus

V. Metag

J. Michel

D.M. Mihaylov

A. Molenda

C. Müntz

R. Münzer

M. Nabroth

L. Naumann

K. Nowakowski

A. Opíchal

J. Orliński

J.-H Otto

Cyprus

Y. Parpottas

M. Parschau

C. Pauly

V. Pechenov

O. Pechenova

K. Piasecki

J. Pietraszko

T. Povar

K. Prościński

A. Prozorov

W. Przygoda

K. Pysz

B. Ramstein

N. Rathod

P. Rodriguez-Ramos

A. Rost

A. Rustamov

P. Salabura

K. Scharmann

T. Scheib

N. Schild

K. Schmidt-Sommerfeld

H. Schuldes

E. Schwab

F. Scozzi

First measurement of massive virtual photon emission from N* baryon resonances

By means of the zero-curvature equation and two sets of Lenard recursion sequences, we construct a nonisospectral generalized 3 × 3 Ablowitz–Kaup–Newell–Segur (AKNS) integrable hierarchy. The general inhomogeneous Dirac–Manakov equations with temporally and spatially modulated coefficients are derived. Under some special reductions, the two-component nonlinear Schrödinger (NLS) or Manakov equations with helicoidal spin-orbit (SO) coupling, Rabi coupling, and mixed helicoidal SO and Rabi couplings are obtained. In particular, we propose several novel inhomogeneous two-component NLS equations which have variable helicoidal SO and Rabi couplings as well as external potentials. The <italic>N</italic>-fold Darboux-dressing transformation related to the nonisospectral generalized 3&#8239;&#215;&#8239;3 AKNS matrix eigenvalue problem is established, and further the <italic>N</italic>-soliton solution represented in a compact determinant form is given. The classification of solitons for a two-component NLS equations with temporally modulated mixed helicoidal SO and Rabi couplings is discussed in detail. Specifically, three types of solitons including beating, bell-shaped and multi-peak solitons as well as their parabolic, periodic, exponential and kinked deformations, and some unconventional nonlinear superpositions are presented.

Jiao Wei

Xin Wang

Yanpei Zhen

Chendi Zhu

Tengjin Zhao

The general integrable inhomogeneous Dirac–Manakov equations: Darboux-dressing transformation and <italic>N</italic>-soliton solutions

We derive a parameter-free geometric constraint on residue phases dictated by the pole-threshold angle. Using the <italic>N</italic>(2190) anomaly as a test case, this constraint reveals a sign ambiguity in prior data; correcting the sign ambiguity yields a phase of <math altimg='si13.svg'><mrow><mo>&#8722;</mo><msup><mn>28</mn><mo>&#8728;</mo></msup><mo>&#177;</mo><msup><mn>10</mn><mo>&#8728;</mo></msup></mrow></math>, matching our prediction. This consistency validates the method as a model-independent diagnostic for distinguishing compact from molecular states, offering a rigorous tool for exotic spectroscopy.

Croatia

S. Ceci

Bosnia and Herzegovina

R. Omerović

H. Osmanović

M. Uroić

M. Vukšić

B. Zauner

Geometric constraint on residue phases: resolving the <italic>N</italic>(2190) anomaly and implications for exotic states