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.

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

As is well known, the chiral Gross-Neveu model at finite density can be solved semiclassically with the help of the chiral spiral mean field. The fermion spectrum has a single gap right at the Fermi energy, a reflection of the Peierls instability. Here, we divide the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math> fermion flavors into two subsets to which we attribute two different densities. The Hartree-Fock ground state of such a system can again be found analytically, using as mean field the “twisted kink crystal” of Basar and Dunne. Its spectrum displays two gaps with lower edges coinciding with the two Fermi energies. This solution is favored over the homogeneous one, providing us with an explicit example of a multiple Peierls instability.

Michael Thies

Peierls instability for systems with several Fermi surfaces: An example from the chiral Gross-Neveu model

We study fermionic instantons of the Gross-Neveu and the Gross-Neveu-Yukawa models. We derive new solutions for both models and examine the corresponding actions at the fixed points. We further map the solutions on to the sphere and discuss the relation to the Hubbard-Stratonovich approach. Close to the fixed points we compare and identify the results with those obtained in the large <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math> computation.

Iran

A. Imaanpur

S.E. Sadati

Instantons in Gross-Neveu and Gross-Neveu-Yukawa models

We extend the particle-flow neural assisted simulations (parnassus) framework of fast simulation and reconstruction to entire collider events. In particular, we use two generative artificial intelligence tools, continuous normalizing flows and diffusion models, to create a set of reconstructed particle-flow objects conditioned on truth-level particles from CMS Open Simulations. While previous work focused on jets, our updated methods now can accommodate all particle-flow objects in an event along with particle-level attributes like particle type and production vertex coordinates. This approach is fully automated, entirely written in Python, and GPU-compatible. Using a variety of physics processes at the LHC, we show that the extended parnassus is able to generalize beyond the training dataset and outperforms the standard, public tool delphes.

Israel

Etienne Dreyer

Eilam Gross

Dmitrii Kobylianskii

United States

Vinicius Mikuni

Benjamin Nachman

Conditional deep generative models for simultaneous simulation and reconstruction of entire events

We investigate the Gross–Llewellyn Smith sum rule within the framework of analytic quantum chromodynamics (QCD). A comparison is performed between experimental data, lattice calculations, and perturbative QCD based on conventional and analytic versions of perturbation theory with different parametrizations for the higher twist contributions. We show that conventional perturbation theory fails to reproduce the data, while the analytic version demonstrates good agreement with experiment and lattice calculations. We also discuss the relation between the Gross–Llewellyn Smith sum rule and the Bjorken sum rule.

JINR

I.R. Gabdrakhmanov

Russia

N. A Gramotkov

A.V. Kotikov

O.V. Teryaev

D.A. Volkova

Chile

I.A. Zemlyakov

Gross–Llewellyn Smith sum rule with an analytic coupling

Event reconstruction at the LHC, the task of assigning observed physics objects to their true origins, is a central challenge for precision measurements and searches. Many existing machine learning approaches address this problem but rely on a single event topology, restricting their applicability to realistic analyses where multiple signal and background processes with different structures are present. To overcome this, we present TIGER, a novel hierarchical graph network that is fundamentally topology agnostic. By incorporating only the common underlying structure of sequential two-body decays, our model can reconstruct complex events without process-specific assumptions. This flexible architecture supports multitask learning, enabling simultaneous event reconstruction and classification. TIGER thus provides a powerful and generalizable tool for physics analysis at the LHC.

Nathalie Soybelman

Nilotpal Kakati

Italy

Francesco A. Di Bello

Topology-agnostic, hierarchical graph network for event reconstruction

We renormalize the Gross-Neveu-Yukawa model with an <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>O</mi><mo stretchy="false">(</mo><mi>N</mi><mo stretchy="false">)</mo></math> symmetry to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">O</mi><mo stretchy="false">(</mo><msup><mi>ε</mi><mn>5</mn></msup><mo stretchy="false">)</mo></math> in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>d</mi><mo>=</mo><mn>4</mn><mo>−</mo><mi>ε</mi></math> dimensions and determine the anomalous dimensions of the fermion and scalar fields, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>β</mi></math> functions as well as the scalar field’s mass operator. These are used to construct several <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math>-dependent critical exponents relevant for quantum transitions in semimetals and in particular those connected with graphene in three dimensions when <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi><mo>=</mo><mn>2</mn></math>. Improved exponent estimates for scalar fermion transitions on a honeycomb lattice, when <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi><mo>=</mo><mn>1</mn></math>, as well as for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi><mo>=</mo><mn>5</mn></math> are also given to compare with results from other techniques such as the conformal bootstrap.

United Kingdom

J.A. Gracey

Spain

A. Maier

P. Marquard

Y. Schröder

Anomalous dimensions and critical exponents for the Gross-Neveu-Yukawa model at five loops

We compute template formulae of all four-loop $\textit{β}$-functions and anomalous dimensions of arbitrary renormalisable quantum field theories with fermions and scalar fields in the $$ \overline{\textrm{MS}} $$ scheme. Using these results, novel contributions to the $\textit{β}$-functions of the Higgs and top coupling are extracted. We discuss how four loops present a challenge to dimensional continuation from four to three dimensions and propose a solution.

Tom Steudtner

Four loop renormalisation group equations in general Gross-Neveu-Yukawa theories

We study the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>O</mi><mo stretchy="false">(</mo><mn>2</mn><mi>N</mi><mo stretchy="false">)</mo></mrow></math> symmetric Gross-Neveu model at finite density in the presence of a <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> chemical potential <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>h</mi></math> for a generic number <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>a</mi><mo>≤</mo><mi>N</mi><mo>−</mo><mn>2</mn></mrow></math> of fermion fields. By combining perturbative quantum field theory, semiclassical large <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math>, and Bethe ansatz techniques, we show that at finite <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math> two new dynamically generated scales <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi mathvariant="normal">n</mi></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi mathvariant="normal">c</mi></msub></math> appear in the theory, governing the mass gap of neutral and charged fermions, respectively. Above a certain threshold value for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>h</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>a</mi></math>-fermion bound states condense and form an inhomogeneous configuration, which at infinite <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math> is a crystal spontaneously breaking translations. At large <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>h</mi></math>, this crystal has mean <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi mathvariant="normal">n</mi></msub></math> and spatial oscillations of amplitude <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi mathvariant="normal">c</mi></msub></math>. The two scales also control the nonperturbative corrections to the free energy, resolving a puzzle concerning fractional-power renormalons and predicting new ones.

Francesco Benini

Ohad Mamroud

Tomás Reis

Marco Serone

Condensates, Crystals, and Renormalons in the Gross-Neveu Model at Finite Density

A novel Bogomol’nyi–Prasad–Sommerfield (BPS) bound for the Gross–Pitaevskii equations in two spatial dimensions is presented herein. The energy can be bounded from below in terms of the combination of two boundary terms, one related to the vorticity (but “dressed” by the condensate profile) and the second to the “skewness” of the configurations. The bound is saturated by configurations that satisfy a system of two first-order partial differential equations. When such a BPS system is satisfied, the Gross–Pitaevskii equations are also satisfied. The analytic solutions of this BPS system in the present manuscript represent configurations with fractional vorticity living in an annulus. Using these techniques, we present the first analytic examples of this kind. The hydrodynamic interpretation of the BPS system is discussed, and the implications of these results are outlined.

Fabrizio Canfora

Czechia

Pablo Pais

A Bogomol’nyi–Prasad–Sommerfield bound with a first-order system in the 2$\textit{D}$ Gross–Pitaevskii equation