We present a neural network wave function framework for solving non-Abelian lattice gauge theories in a continuous group representation. Using a combination of SU(2) equivariant neural networks alongside an SU(2) invariant, physics-inspired ansatz, we learn a parametrization of the ground state wave function of SU(2) lattice gauge theory in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>2</mn><mo>+</mo><mn>1</mn></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>3</mn><mo>+</mo><mn>1</mn></mrow></math> dimensions. Our method, performed in the Hamiltonian formulation, has a straightforward generalization to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>SU</mi><mo stretchy="false">(</mo><mi>N</mi><mo stretchy="false">)</mo></mrow></math>. We benchmark our approach against a solely invariant ansatz by computing the ground state energy, demonstrating the need for bespoke gauge equivariant transformations. We evaluate the Creutz ratio and average Wilson loop, and obtain results in strong agreement with perturbative expansions. Our method opens up an avenue for studying lattice gauge theories beyond one dimension, with efficient scaling to larger systems, and in a way that avoids both the sign problem and any discretization of the gauge group.

Netherlands

Thomas Spriggs

Eliska Greplova

Switzerland

Juan Carrasquilla

Jannes Nys

Accurate Ground States of SU(2) Lattice Gauge Theory in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>2</mn><mo>+</mo><mn>1</mn><mi mathvariant="normal">D</mi></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>3</mn><mo>+</mo><mn>1</mn><mi mathvariant="normal">D</mi></mrow></math>

A reliable calculation of radiative corrections to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>τ</mi><mo stretchy="false">→</mo><mi>π</mi><mi>π</mi><msub><mrow><mi>ν</mi></mrow><mrow><mi>τ</mi></mrow></msub></mrow></math> decays is an important prerequisite for using hadronic <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>τ</mi></math> decays for a data-driven evaluation of the hadronic-vacuum-polarization (HVP) contribution to the anomalous magnetic moment of the muon, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mi>a</mi></mrow><mrow><mi>μ</mi></mrow><mrow><mi>HVP</mi><mo>,</mo><mi>LO</mi></mrow></msubsup><mo stretchy="false">[</mo><mi>π</mi><mi>π</mi><mo>,</mo><mi>τ</mi><mo stretchy="false">]</mo></mrow></math>. In this Letter, we present an improved model-independent analysis of these radiative corrections, including, for the first time, effects beyond pointlike pions in the evaluation of the loop diagrams. These structure-dependent corrections, implemented via a dispersive representation of the pion form factor, lead to significant changes compared to previous calculations due to enhancements near the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>ρ</mi><mo stretchy="false">(</mo><mn>770</mn><mo stretchy="false">)</mo></mrow></math> resonance. We also devise strategies for the matching to chiral perturbation theory and a stable implementation of the real corrections down to the two-pion threshold, which shows that some higher-order isospin-breaking corrections need to be kept due to a strong threshold enhancement. Finally, we perform dispersive fits to the currently available <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>τ</mi><mo stretchy="false">→</mo><mi>π</mi><mi>π</mi><msub><mrow><mi>ν</mi></mrow><mrow><mi>τ</mi></mrow></msub></mrow></math> spectra and discuss the consequences for isospin-breaking corrections in the evaluation of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mi>a</mi></mrow><mrow><mi>μ</mi></mrow><mrow><mi>HVP</mi><mo>,</mo><mi>LO</mi></mrow></msubsup><mo stretchy="false">[</mo><mi>π</mi><mi>π</mi><mo>,</mo><mi>τ</mi><mo stretchy="false">]</mo></mrow></math>.

Gilberto Colangelo

Martina Cottini

Martin Hoferichter

Simon Holz

Improved Calculation of Radiative Corrections to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>τ</mi><mo stretchy="false">→</mo><mi>π</mi><mi>π</mi><msub><mrow><mi>ν</mi></mrow><mrow><mi>τ</mi></mrow></msub></mrow></math> Decays

The energy density generated by a vector current is characterized by a single parameter <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>a</mi><mi mathvariant="script">E</mi></msub></math> bounded by unitarity to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo>−</mo><mn>1</mn><mo>/</mo><mn>2</mn><mo>≤</mo><msub><mrow><mi>a</mi></mrow><mrow><mi mathvariant="script">E</mi></mrow></msub><mo>≤</mo><mn>1</mn></mrow></math>, with extremal values saturated by free theories of different matter content. Through confinement, QCD transmutes fermionic matter into scalars, revealing a nontrivial flow between extremal correlators. We reconstruct this flow using perturbative QCD and chiral perturbation theory. The observable is accessible with currently available experimental data.

CERN

Marc Riembau

South Korea

Minho Son

Flow between Extremal One-Point Energy Correlators in QCD

Neutron star mergers provide a unique laboratory for the study of strong-field gravity coupled to quantum chromodynamics in extreme conditions. The frequencies and amplitudes of the resulting gravitational waves encode invaluable information about the merger. Simulations to date have shown that these frequencies lie in the kilohertz range. They have also shown that, if quantum chromodynamics possesses a first-order phase transition at high baryon density, then this is likely to be accessed during the merger dynamics. Here, we show that this would result in the nucleation of superheated and/or supercompressed bubbles whose subsequent dynamics would produce gravitational waves in the megahertz range. We estimate the amplitude of this signal and compare it to the sensitivity of planned future detectors.

Spain

Diego Blas

Jorge Casalderrey-Solana

David Mateos

France

Mikel Sanchez-Garitaonandia

Megahertz Gravitational Waves from Neutron Star Mergers

We propose that the broad architecture of the renormalization group flow in quantum field theories is, at least in part, fixed by unitarity. The precise statement is summarized in the unitarity flow conjecture, which states that the nonlinear <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>S</mi></mrow></math>-matrix identities obtained by imposing unitarity imply those needed to derive the renormalization group equations. As a proof of principle, we verify this conjecture to all loops at the leading and subleading logarithmic order in the four-dimensional massless <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>λ</mi><msup><mrow><mi>ϕ</mi></mrow><mrow><mn>4</mn></mrow></msup></mrow></math> theory using on-shell techniques, without reference to any counterterms or Feynman diagrams.

United States

Ameya Chavda

Daniel McLoughlin

Sebastian Mizera

John Staunton

Unitarity Flow Conjecture: An On-Shell Approach to the Renormalization Group

We provide arguments indicating that the semiclassical Einstein equations follow from quantum relative entropy and its proportionality to an area variation. Using modular theory, we establish that the relative entropy between the vacuum state and coherent excitations of a scalar quantum field on a bifurcate Killing horizon is given by the energy flux across the horizon. Under the assumption of the Bekenstein-Hawking entropy-area formula, this energy flux is proportional to a variation in the surface area of the horizon cross section. The semiclassical Einstein equations follow automatically from this identification. Our approach provides a quantum field theoretic generalization of Jacobson’s thermodynamic derivation of the Einstein equations, replacing classical thermodynamic entropy with the well-defined quantum relative (Araki-Uhlmann) entropy. This suggests that quantum information plays a central role in what is often seen as a zeroth order approximation of a theory of quantum gravity, namely quantum field theory in curved spacetimes.

Germany

Philipp Dorau

Albert Much

From Quantum Relative Entropy to the Semiclassical Einstein Equations

We present the first successful large-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math> computation of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>S</mi><mn>3</mn></msup></math> free energy in chiral <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">N</mi><mo>=</mo><mn>2</mn></math> Chern-Simons-matter theories, long believed to evade the universal M2-brane scaling <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>F</mi><msup><mi>S</mi><mn>3</mn></msup></msub><mo>∼</mo><msup><mi>N</mi><mrow><mn>3</mn><mo>/</mo><mn>2</mn></mrow></msup></math>. Using a stable numerical continuation method that directly solves the saddle-point equations, we obtain convergent large-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math> solutions for benchmark chiral quivers, including the holographic dual to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>AdS</mi></mrow><mrow><mn>4</mn></mrow></msub><mo>×</mo><msup><mi>Q</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msup><mo>/</mo><msub><mi mathvariant="double-struck">Z</mi><mi>k</mi></msub></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>D</mi><mn>3</mn></msub></math> models. The resulting free energies precisely match the holographic predictions, resolving a decade-old puzzle in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>AdS</mi></mrow><mrow><mn>4</mn></mrow></msub><mo>/</mo><msub><mrow><mi>CFT</mi></mrow><mn>3</mn></msub></mrow></math> and establishing a practical numerical framework for precision holography in strongly coupled gauge theories.

United Kingdom

Seyed Morteza Hosseini

Large-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math> Free Energy of Chiral <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">N</mi><mo>=</mo><mn>2</mn></math> Chern-Simons-Matter Theories

We suggest that the chiral <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo stretchy="false">(</mo><msub><mrow><mi mathvariant="fraktur">e</mi></mrow><mrow><mn>8</mn></mrow></msub><msub><mrow><mo stretchy="false">)</mo></mrow><mrow><mn>1</mn></mrow></msub></mrow></math> theory—in many senses the simplest vertex operator algebra—may have Haagerup symmetry <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi mathvariant="script">H</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></math> for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>i</mi><mo>=</mo><mn>1</mn></math>, 2, 3. Likewise, we suggest that the nonchiral <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><msub><mi>E</mi><mn>8</mn></msub><msub><mo stretchy="false">)</mo><mn>1</mn></msub></math> Wess-Zumino-Witten model may have <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi mathvariant="script">H</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>×</mo><msubsup><mrow><mi mathvariant="script">H</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi>op</mi></mrow></msubsup></mrow></math> symmetry, and that gauging the diagonal symmetry gives a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>c</mi><mo>=</mo><mn>8</mn></math> theory with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mrow><mi mathvariant="script">Z</mi></mrow><mo stretchy="false">(</mo><msub><mrow><mi mathvariant="script">H</mi></mrow><mrow><mn>3</mn></mrow></msub><mo stretchy="false">)</mo></mrow></math> symmetry, which is the theory predicted in Evans and Gannon [<a href="http://dx.doi.org/10.1007/s00220-011-1329-3">Commun. Math. Phys. 307, 463 (2011)</a>]. Along the way, we show that <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><msub><mi>E</mi><mn>8</mn></msub><msub><mo stretchy="false">)</mo><mn>1</mn></msub></math> also has a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>Fib</mi><mo>×</mo><msup><mrow><mi>Fib</mi></mrow><mrow><mi>op</mi></mrow></msup></mrow></math> symmetry, and that gauging the diagonal symmetry gives the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><msub><mi>G</mi><mn>2</mn></msub><msub><mo stretchy="false">)</mo><mn>1</mn></msub><mo>×</mo><mo stretchy="false">(</mo><msub><mi>F</mi><mn>4</mn></msub><msub><mo stretchy="false">)</mo><mn>1</mn></msub></math> Wess-Zumino-Witten model, explaining the well-known conformal embedding <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><msub><mi>G</mi><mn>2</mn></msub><msub><mo stretchy="false">)</mo><mn>1</mn></msub><mo>×</mo><mo stretchy="false">(</mo><msub><mi>F</mi><mn>4</mn></msub><msub><mo stretchy="false">)</mo><mn>1</mn></msub><mo>⊂</mo><mo stretchy="false">(</mo><msub><mi>E</mi><mn>8</mn></msub><msub><mo stretchy="false">)</mo><mn>1</mn></msub></math>. Finally, we suggest a relation to theories with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi mathvariant="script">H</mi></mrow><mrow><mn>3</mn></mrow></msub></mrow></math> symmetry at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>c</mi><mo>=</mo><mn>2</mn></math>, 6, complimenting the discussion with new modular bootstrap results.

Jan Albert

Japan

Yamato Honda

Justin Kaidi

China

Yunqin Zheng

Haagerup Symmetry in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo stretchy="false">(</mo><msub><mrow><mi>E</mi></mrow><mrow><mn>8</mn></mrow></msub><msub><mrow><mo stretchy="false">)</mo></mrow><mrow><mn>1</mn></mrow></msub></mrow></math>?

The Hawking radiation spectrum from a collapsing null shell can be derived via the double copy of a simpler gauge theory calculation. Analyzing the non-Abelian Yang-Mills root of this process, we demonstrate that the radiation spectrum is thermal in the color charge eigenvalue <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>λ</mi></math>, not energy. Considering the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>SU</mi><mo stretchy="false">(</mo><msub><mrow><mi>N</mi></mrow><mrow><mi>c</mi></mrow></msub><mo stretchy="false">)</mo></mrow></math> gauge theory in the large <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>c</mi></msub></math> limit, we find the differential spectrum <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">d</mi><mi>N</mi><mo>/</mo><mi mathvariant="normal">d</mi><mi>λ</mi></math> is a product of the gravitationally familiar Planck-like factor and the color phase space density, modeled here as the Wigner semicircle from random matrix theory. This reveals that apparent energy thermality in gravity is the direct dual of charge thermality in its underlying non-abelian gauge theory.

John Joseph M. Carrasco

Yaxi Chen

Double Copy Root of Hawking Thermality

Gravity and gauge theory are concretely linked by the double copy. Although well-studied at the level of perturbative scattering in vacuum, far less is known about nonperturbative aspects or extensions of double copy beyond trivial backgrounds. We show here how Hawking radiation in a collapse metric, its associated thermal spectrum, and horizon dependence, emerges from the double copy of particle production in a background gauge field, where there is no global horizon or thermal spectrum. Our approach combines worldline and amplitude methods, and allows the unification of several classical and quantum double copy prescriptions for black hole spacetimes.

Anton Ilderton

William Lindved

Karthik Rajeev

Hawking Radiation from the Double Copy