Using accurate computational methods, we compute the quasinormal frequencies of a massive scalar field propagating near a black hole in the framework of non-minimal Einstein–Yang–Mills theory with a non-zero cosmological constant. We show that increasing the mass of the scalar field significantly decreases the damping rate of the quasinormal modes for both asymptotically flat and de Sitter black holes. However, in the de Sitter case, arbitrarily long-lived modes can exist, whereas in the asymptotically flat case, the damping rate never vanishes completely. In the limit of quasi-resonances, we observe a kind of universal behavior where the frequencies do not depend on the coupling constant. Applying the time-domain integration of perturbation equations we show that even when the effective potential has a negative gap, the scalar field is stable and the perturbations decay in time. In the regime of large mass of the field we obtain the analytic formula for quasinormal modes.

Spain

Alexey Dubinsky

Long-lived quasinormal modes and quasi-resonances around non-minimal Einstein–Yang–Mills black holes

The path integral over massless quantum fields in Minkowski space with scattering boundary conditions defines a Carrollian partition function on the null boundary. We develop this framework for non-Abelian gauge theory, both from a general perspective and through explicit examples that highlight subtle aspects of soft modes and asymptotic symmetries. These include falloff conditions, Goldstone modes and their antipodal matching, and factors of two associated with conditionally convergent integrals arising in the derivation of soft theorems. We employ path integral (rather than canonical) methods throughout.

United States

Per Kraus

Richard Myers

Carrollian partition function for bulk Yang-Mills theory

We clarify the origin of magic angles in twisted multilayered graphene using Yang-Mills flows in two dimensions. We relate the effective Hamiltonian describing the electrons in the multilayered graphene to the $$ {\overline{\partial}}_A $$ operator on a two dimensional torus coupled to an SU($\textit{N}$) gauge field. Despite the absence of a characteristic class such as $\textit{c}$ relevant for the quantum Hall effect, we show that there are topological invariants associated with the zero modes occuring in a family of Hamiltonians. The flatbands in the spectrum of the effective Hamiltonian are associated with Yang-Mills connections, studied by M. Atiyah and R. Bott long time ago. The emergent U(1) magnetic field with nonzero flux is presumably responsible for the observed Hall effect in the absence of (external) magnetic field. We provide a numeric algorithm transforming the original single-particle Hamiltonian to the direct sum of $$ {\overline{\partial}}_A $$ operators coupled to abelian gauge fields with non-zero $\textit{c}$ ’s. Our gradient flow perspective gives a simple bound for magic angles: if the gauge field $\textit{A}$($\textit{α}$) is such that the YM energy $$ {\int}_{{\mathbbm{T}}^2} $$ tr $$ {F}_{A\left(\alpha \right)}^2 $$ is smaller than that of U(1) magnetic flux embedded into SU(2), then $\textit{α}$ is not magic.

Vasilii Iugov

Nikita Nekrasov

Yang-Mills flows for multilayered graphene

<p>We apply the variational Monte Carlo method based on neural network quantum states, using a neural autoregressive flow architecture as our ansatz, to determine the ground state wave function of the bosonic <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> Yang-Mills-type two-matrix model at strong coupling. Previous literature hinted at the inaccuracy of such an approach at strong coupling. In this work, the accuracy of the results is tested using lattice Monte Carlo simulations: we benchmark the expectation value of the energy of the ground state for system sizes <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math> that are beyond brute-force exact diagonalization methods. We observe that the variational method with neural network states reproduces the right ground state energy when the width of the network employed in this work is sufficiently large. We confirm that the correct result is obtained for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi><mo>=</mo><mn>2</mn></math> and 3, while obtaining a precise value for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi><mo>=</mo><mn>4</mn></math> requires more resources than the amount available for this work.</p>

Germany

Norbert Bodendorfer

Türkiye

Onur Oktay

United Kingdom

Vaibhav Gautam

Masanori Hanada

Japan

Enrico Rinaldi

Variational Monte Carlo with neural network quantum states for a Yang-Mills matrix model

In recent work Amorosso et al. (2024), we computed a novel flux tube entanglement entropy (FTE) of the color flux tube stretched between a heavy quark-antiquark pair on a Euclidean lattice in (2+1)D Yang–Mills theory. Our numerical results suggested that FTE can be partitioned into an internal color entanglement entropy and a vibrational entropy corresponding to the transverse excitations of a QCD string, with the latter described by a thin string model. Since the color flux tube does not have transverse excitations in (1+1)D Yang–Mills theory, we use this simpler framework to perform an exact analytical computation of the contribution of the internal color degrees of freedom to FTE. For the multipartite partitioning of the color flux tube, we find the remarkable result that FTE depends only on the dimension of the color group representation and the number of times the flux tube crosses the boundary between the traced and untraced spatial regions but not on the string length. Our proof is independent of whether the replica and region boundaries on the lattice are placed on vertices or in plaquette centers.

Rocco Amorosso

Sergey Syritsyn

Raju Venugopalan

Entanglement entropy of a color flux tube in (1+1)D Yang–Mills theory

<p>Motivated by the deviations observed between the experimental measurements and the Standard Model (SM) predictions of the branching ratios of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover><mi>s</mi><mn>0</mn></msubsup><mo stretchy="false">→</mo><msubsup><mi>D</mi><mi>s</mi><mo>+</mo></msubsup><msup><mi>π</mi><mo>−</mo></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover><mi>d</mi><mn>0</mn></msubsup><mo stretchy="false">→</mo><msup><mi>D</mi><mo>+</mo></msup><msup><mi>K</mi><mo>−</mo></msup></math> decays, we revisit the two-body hadronic <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>B</mi><mi>c</mi><mo>−</mo></msubsup><mo stretchy="false">→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><mo stretchy="false">(</mo><msub><mi>η</mi><mi>c</mi></msub><mo stretchy="false">)</mo><msup><mi>L</mi><mo>−</mo></msup></math> decays, with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>L</mi><mo>=</mo><mi>π</mi><mo>,</mo><msup><mi>K</mi><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup><mo>,</mo><mi>ρ</mi></math>, both within the SM and beyond. Since these processes are also mediated by the quark-level <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>b</mi><mo stretchy="false">→</mo><mi>c</mi><mover accent="true"><mi>u</mi><mo stretchy="false">¯</mo></mover><mi>d</mi><mo stretchy="false">(</mo><mi>s</mi><mo stretchy="false">)</mo></math> transitions and hence dominated by the color-allowed tree topology, the QCD factorization is generally expected to hold in the heavy-quark limit. First, we update the SM predictions of the observables of these decays by including the nonfactorizable vertex corrections to the hadronic matrix elements of the SM four-quark operators up to the next-to-next-to-leading order (NNLO) in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>α</mi><mi>s</mi></msub></math>. It is found that, relative to the leading-order results, the branching ratios of these decays up to the next-to-leading-order (NLO) and NNLO corrections are always enhanced, with a relative amount given by <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>δ</mi><mi>NLO</mi></msub><mo>=</mo><mo stretchy="false">(</mo><msup><mi mathvariant="script">B</mi><mi>NLO</mi></msup><mo>−</mo><msup><mi mathvariant="script">B</mi><mi>LO</mi></msup><mo stretchy="false">)</mo><mo>/</mo><msup><mi mathvariant="script">B</mi><mi>LO</mi></msup><mo>≈</mo><mo>+</mo><mn>6</mn><mo>%</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>δ</mi><mrow><mi>NNLO</mi></mrow></msub><mo>=</mo><mo stretchy="false">(</mo><msup><mi mathvariant="script">B</mi><mrow><mi>NNLO</mi></mrow></msup><mo>−</mo><msup><mi mathvariant="script">B</mi><mi>LO</mi></msup><mo stretchy="false">)</mo><mo>/</mo><msup><mi mathvariant="script">B</mi><mi>LO</mi></msup><mo>≈</mo><mo>+</mo><mn>9</mn><mo>%</mo></math>, respectively. To minimize the uncertainties brought by the Cabibbo-Kobayashi-Maskawa matrix element <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>V</mi><mrow><mi>c</mi><mi>b</mi></mrow></msub></math> as well as the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>B</mi><mi>c</mi></msub><mo stretchy="false">→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><mo stretchy="false">(</mo><msub><mi>η</mi><mi>c</mi></msub><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>B</mi><mrow><mo stretchy="false">(</mo><mi>s</mi><mo stretchy="false">)</mo></mrow></msub><mo stretchy="false">→</mo><msubsup><mi>D</mi><mrow><mo stretchy="false">(</mo><mi>s</mi><mo stretchy="false">)</mo></mrow><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msubsup></math> transition form factors, we construct ratios of the nonleptonic decay rates with respect to the corresponding differential semileptonic decay rates evaluated at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>q</mi><mn>2</mn></msup><mo>=</mo><msubsup><mi>m</mi><mi>L</mi><mn>2</mn></msubsup></math> (for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>R</mi><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi><mo stretchy="false">(</mo><msub><mi>η</mi><mi>c</mi></msub><mo stretchy="false">)</mo><mi>L</mi></mrow></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>R</mi><mrow><mo stretchy="false">(</mo><mi>s</mi><mo stretchy="false">)</mo><mi>L</mi></mrow><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msubsup></math>) or integrated over the whole <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>q</mi><mn>2</mn></msup></math> range (for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>R</mi><mrow><mi>π</mi><mo>/</mo><mi>μ</mi><msub><mi>ν</mi><mi>μ</mi></msub></mrow></msub></math>), which are then used to constrain the model-independent new physics (NP) Wilson coefficients. After considering the latest Belle data on <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover><mn>0</mn></msup><mo stretchy="false">→</mo><msup><mi>D</mi><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo><mo>+</mo></mrow></msup><mi>π</mi><mo stretchy="false">(</mo><mi>K</mi><msup><mo stretchy="false">)</mo><mo>−</mo></msup></math> decays and the updated fitting results of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>B</mi><mrow><mo stretchy="false">(</mo><mi>s</mi><mo stretchy="false">)</mo></mrow></msub><mo stretchy="false">→</mo><msubsup><mi>D</mi><mrow><mo stretchy="false">(</mo><mi>s</mi><mo stretchy="false">)</mo></mrow><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msubsup></math> transition form factors, we find that the deviations can still be explained by the NP four-quark operators with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><mn>1</mn><mo>+</mo><msub><mi>γ</mi><mn>5</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">⊗</mo><mo stretchy="false">(</mo><mn>1</mn><mo>−</mo><msub><mi>γ</mi><mn>5</mn></msub><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><mn>1</mn><mo>+</mo><msub><mi>γ</mi><mn>5</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">⊗</mo><mo stretchy="false">(</mo><mn>1</mn><mo>+</mo><msub><mi>γ</mi><mn>5</mn></msub><mo stretchy="false">)</mo></math> structures, while the solution with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>γ</mi><mi>μ</mi></msup><mo stretchy="false">(</mo><mn>1</mn><mo>+</mo><msub><mi>γ</mi><mn>5</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">⊗</mo><msub><mi>γ</mi><mi>μ</mi></msub><mo stretchy="false">(</mo><mn>1</mn><mo>−</mo><msub><mi>γ</mi><mn>5</mn></msub><mo stretchy="false">)</mo></math> structure does not work anymore, under the combined constraints from the ratios <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>R</mi><mrow><mo stretchy="false">(</mo><mi>s</mi><mo stretchy="false">)</mo><mi>L</mi></mrow><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msubsup></math> at the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>2</mn><mi>σ</mi></math> level. Furthermore, the ratio <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>R</mi><mrow><mi>π</mi><mo>/</mo><mi>μ</mi><msub><mi>ν</mi><mi>μ</mi></msub></mrow></msub></math>, once measured precisely, could provide complementary constraint on these NP Wilson coefficients allowed by <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>R</mi><mrow><mo stretchy="false">(</mo><mi>s</mi><mo stretchy="false">)</mo><mi>L</mi></mrow><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msubsup></math>. With the large <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>B</mi><mi>c</mi></msub></math> events expected at the Large Hadron Collider, we hope to obtain more precise measurements of these observables, which can be exploited to discriminate the different NP scenarios responsible for the deviations observed in the two-body nonleptonic <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi></math>-meson decays.</p>

China

Wei-Jun Deng

Fang-Min Cai

Xin-Qiang Li

Yan Shi

Ya-Dong Yang

Revisiting <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>B</mi><mi>c</mi><mo>−</mo></msubsup><mo stretchy="false">→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><mo stretchy="false">(</mo><msub><mi>η</mi><mi>c</mi></msub><mo stretchy="false">)</mo><msup><mi>L</mi><mo>−</mo></msup></math> decays within the SM and beyond in QCD factorization

We construct defect networks in pure Yang-Mills theory in two dimensions using a refinement of the lattice approach. The refinement preserves the locality properties of individual defects, and is compatible with solvability of the theory via subdivision invariance. We explicitly demonstrate closure of the building blocks under fusion.

Italy

Luca Griguolo

Elisa Marieni

Itamar Yaakov

Lattice defect networks in 2d Yang-Mills

We propose that chiral two-dimensional Yang-Mills theory on a Riemann surface is dual to a deformed stationary subsector of the Gromov-Witten theory of that surface. Firstly, we argue that the algebraic structure that underlies the large $\textit{N}$ limit of the chiral gauge theory is a partial permutation algebra of observables which codes covering maps of all degrees simultaneously. Secondly, we exploit the Gromov-Witten/Hurwitz correspondence to interpret chiral Yang-Mills theory as a finite deformation of a Gromov-Witten theory by an area-dependent transposition interaction and an operator that codes a compactification of Hurwitz space. The proposed string dual manifestly includes an integral over the moduli space of Riemann surfaces as well as the identification of closed string states as completed cycles.

France

Lior Benizri

Jan Troost

The string dual to two-dimensional Yang-Mills theory

We perform a detailed computation of key quantities across the first-order deconfinement phase transition of the SU(3) Yang-Mills theory. Specifically, we calculate the entropy density, <math altimg='si1.svg'><mi>s</mi><mo stretchy='false'>(</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>c</mi></mrow></msub><mo stretchy='false'>)</mo><mo stretchy='false'>/</mo><msubsup><mrow><mi>T</mi></mrow><mrow><mi>c</mi></mrow><mrow><mn>3</mn></mrow></msubsup></math>, on both sides of the transition and determine the latent heat <italic>h</italic>. The calculations are carried out in the lattice regularization with the Wilson action, employing shifted boundary conditions in the temporal direction. Our simulations are performed at five different values of the lattice spacing in order to extrapolate the results to the continuum limit. The latent heat can be measured also as the discontinuity in the trace anomaly of the energy-momentum tensor: our result using the entropy density is compatible with the one obtained from the trace anomaly, giving a combined estimate <math altimg='si2.svg'><mi>h</mi><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><mn>1.175</mn><mo stretchy='false'>(</mo><mn>10</mn><mo stretchy='false'>)</mo></math>. Additionally, we determine the critical temperature <math altimg='si3.svg'><msub><mrow><mi>T</mi></mrow><mrow><mi>c</mi></mrow></msub></math> in physical units with permille accuracy, yielding <math altimg='si4.svg'><msub><mrow><mi>T</mi></mrow><mrow><mi>c</mi></mrow></msub><msqrt><mrow><msub><mrow><mi>t</mi></mrow><mrow><mn>0</mn></mrow></msub></mrow></msqrt><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><mn>0.24915</mn><mo stretchy='false'>(</mo><mn>29</mn><mo stretchy='false'>)</mo></math>. These results allow to connect with precision the confined and the deconfined phases and we present an improved computation of the Equation of State across the deconfinement transition for <italic>T</italic> between 0 and <math altimg='si5.svg'><mn>3.4</mn><msub><mrow><mi>T</mi></mrow><mrow><mi>c</mi></mrow></msub></math>.

Leonardo Giusti

Mitsuaki Hirasawa

Michele Pepe

Luca Virzì

A precise study of the thermodynamic properties of the SU(3) Yang-Mills theory across the deconfinement transition

We use a loop truncated Jevicki-Sakita effective collective field Hamiltonian to obtain, over a very large range of values of 't Hooft's coupling, and directly in the large <italic>N</italic> limit, the large <italic>N</italic> (planar) ground state energy, the planar ground state expectation values of invariant correlators, and the <math altimg='si1.svg'><mn>1</mn><mo stretchy='false'>/</mo><mi>N</mi></math> spectrum of the quantum mechanical system of three massless Yang-Mills coupled matrices. This captures the dynamics of the (residual) gauge invariant sector of the spatially reduced <math altimg='si2.svg'><mn>3</mn><mo linebreak='goodbreak' linebreakstyle='after'>+</mo><mn>1</mn></math> dimensional pure Yang-Mills theory, in the large <italic>N</italic> limit. The large <italic>N</italic> loop space constraints are handled by the use of master variables. As is the case for two matrices, the method is highly efficient directly in the massless limit, and it reproduces to a very high precision the scaling dependence of physical quantities, determined by their dimensions, on the dimensionful 't Hooft coupling. We obtain the bound state masses of &#8220;glueballs&#8221;, their quantum numbers and ensuing degeneracies.

South Africa

João P. Rodrigues

“Glueballs” in the quantum mechanics of three large massless Yang-Mills coupled matrices