As one of the key targets for future space-based gravitational wave detectors, extreme-mass-ratio inspirals (EMRIs) offer valuable observational clues for testing strong-field gravity and classifying black holes through their orbital dynamics and gravitational wave emission characteristics. This work systematically investigates the transitional periodic orbits of test particles and their single-cycle gravitational radiation features in the background of non-minimally coupled Einstein–Yang–Mills (EYM) BHs. The results show that as the magnetic charge parameter $$Q$$ and the non-minimal coupling constant $$\xi $$ increase, the radii of the marginally bound orbit ( $$r_{\text {MBO}}$$ ) and the innermost stable circular orbit ( $$r_{\text {ISCO}}$$ ) decrease significantly, with corresponding reductions in the orbital energy $$E$$ and angular momentum $$L$$ . Furthermore, the allowable parameter space of energy and angular momentum ( $$E$$ – $$L$$ ) for bound orbits shifts towards the left. We then plot typical periodic orbits through orbit classification, finding that the non-minimal coupling effect suppresses the orbital contraction induced by the magnetic charge, leading to degeneracy of orbits with different $$Q$$ values towards the Schwarzschild case, as well as phase shifts, amplitude enhancement, and period shortening in the gravitational waveforms with increasing $$Q$$ and $$\xi $$ . These results provide theoretical predictions for distinguishing different BH models through future gravitational wave observations.

China

Xiuqin He

Zhaoyi Xu

Meirong Tang

Non-minimally coupled Einstein–Yang–Mills black holes: periodic orbits and gravitational wave radiation in extreme mass ratio systems

We study the spin chain model which captures the one-loop spectral problem of a prototypical example of an <math altimg='si16.svg'><mrow><mi mathvariant='script'>N</mi><mo linebreak='goodbreak'>=</mo><mn>2</mn></mrow></math> SCFT in four dimensions. Up to date, this spin chain model remains unfathomable; the standard coordinate Bethe Ansatz does not lead to a solution from three magnons on, as the Yang-Baxter equation is not satisfied by the two-magnon scattering coefficients. In this paper, we find a long-range solution to the eigenvalue problem for three magnons. Remarkably, the scattering coefficients of particular subclasses of our solution, together with the position-dependent corrections, obey an infinite tower of modified Yang-Baxter equations. Our method of solving the three-magnon problem is interesting in its own right and generalizes the standard coordinate Bethe Ansatz approach to cases where the permutation symmetry is broken.

Germany

Deniz N Bozkurt

Juan Miguel Nieto García

Elli Pomoni

Long-range to the rescue of Yang-Baxter

We give a physical interpretation for the analytic continuation of the partition function of superconformal SU(2) 𝒩 = 2 gauge theory on the four-sphere to all values of the Yang-Mills coupling. We show that a well-motivated 2d construction associates two-dimensional unstable instantons to the 4d complex saddles which appear as singularities in the integrand of the supersymmetric localization expression. The construction is based on the chiral algebra subsector, and aligns with the alternative Higgs branch localization.

United Kingdom

Inês Aniceto

James Ratcliffe

Itamar Yaakov

The resurgence of errors in the localization of 𝒩 = 2 superconformal Yang-Mills

The space-time geometry under investigation is chosen to be a high-dimensional, static, spherically symmetric solution in an asymptotically flat background within the Einstein–power–Yang–Mills–Gauss–Bonnet (EPYMGB) gravity. To address the limitations of previous shadow constraints, we construct a standardized framework based on the Schwarzschild-Tangherlini metric to constrain the characteristic parameters. Additionally, we provide a rigorous derivation of the shadow radius formula for a general high-dimensional spherically symmetric black hole. Subsequently, we systematically and comprehensively present the effective potential equations governing spin-0, spin-1, $\textit{p}$-form, and spin-2 perturbations in high-dimensional static spherically symmetric flat space-time. Our analysis reveals that the Yang–Mills magnetic charge $$\mathcal {Q}$$ and the power $\textit{q}$ have a negligible impact on both the shadow radius and perturbations of the black hole when compared to the Gauss–Bonnet coupling constant $${\alpha }_2$$ in various dimensions. Hence, the physical signatures of the parameters $$\mathcal {Q}$$ and $\textit{q}$ in the black hole environment remain undetectable through either perturbation analysis or shadow observations. Cross-validation of the allowable range of $${\alpha }_2$$ derived from the high-dimensional constraint on shadow radius and the dynamical stability analysis of gravitational perturbations demonstrates excellent agreement between these independent approaches. The conclusions derived from the cross-analysis further substantiate the validity of the high-dimensional shadow constraint formula proposed in this work and indicate that the duality between black hole shadows and perturbations may persist in high-dimensional space-times.

Zening Yan

Constraints on shadow radius and instabilities arising from various perturbations in spherically symmetric black holes in Einstein–power–Yang–Mills–Gauss–Bonnet gravity

In earlier work we proposed a string theory dual to two dimensional Yang-Mills theory at zero coupling (which can also be thought of as a $\textit{BF}$ theory), given by a Polyakov-like generalization of Hořava’s topological rigid string theory, and we showed that it correctly reproduces (in the 1/$\textit{N}$ expansion) several partition functions of $\textit{SU}$ ($\textit{N}$) Yang-Mills theory. In the present paper, we generalise this to Wilson loop expectation values by adding boundaries with one Dirichlet and one Neumann boundary condition to our string worldsheets. We discuss in detail several examples, including examples where the worldsheet has branch points or orientation-reversing tubes, or where the Wilson loop has one or more self-intersections, and we show that in all of them the string theory reproduces the known Yang-Mills expectation values. We argue that examples with orientation-reversing tubes or self-intersecting Wilson loops cannot be brought to the conformal gauge, so we analyse them in a different gauge.

Israel

Ofer Aharony

Italy

Suman Kundu

Tal Sheaffer

A string theory for two dimensional Yang-Mills theory. Part II

We provide a detailed analysis of the gravitational wave spectrum of $\textit{SU}$($\textit{N}$) pure Yang-Mills theory. The confinement phase transition is described with an effective Polyakov loop model, using the latest lattice data as an input. In particular, recent lattice studies clarified the large-$\textit{N}$ scaling of the surface tension, which we incorporate through a modification of the kinetic term. We demonstrate that the thin-wall approximation agrees with the Polyakov loop model at small $\textit{N}$ while it breaks down at large $\textit{N}$. Furthermore, we include reliable estimates of the bubble wall velocity using a recently developed framework based on a large enthalpy jump at the phase transition. Altogether, this allows us to derive the gravitational wave signals for all $\textit{SU}$($\textit{N}$) confinement phase transitions and clarifies the behaviour at large $\textit{N}$ . The strongest signal arises for $\textit{N}$ = 20, but overall the predicted signals remain rather weak. Our work paves the way for future studies of other gauge groups and systems with fermions.

Stephan Huber

Rory Phipps

Manuel Reichert

Gravitational waves from confinement in $\textit{SU}$($\textit{N}$) Yang-Mills theory

We investigate the finite-temperature SU(2) Savvidy model under an imaginary angular velocity. Employing the background-field method, we derive the one-loop effective potential and analyze both its real and imaginary parts. We demonstrate that imaginary rotation modifies the chromomagnetic condensate and the Polyakov loop, and can partially suppress the Nielsen-Olesen instability of the chromomagnetic background. Moreover, a high-temperature expansion shows that imaginary rotation strengthens the effective coupling and that the chromomagnetic field induces a negative contribution to the moment of inertia.

Hao-Lei Chen

Xu-Guang Huang

Chromomagnetic condensate in finite-temperature SU(2) Yang-Mills theory under an imaginary rotation

Homogeneous and isotropic equilibrium states of strongly coupled <math altimg='si2.svg'><mrow><mi mathvariant='script'>N</mi><mo linebreak='goodbreak'>=</mo><mn>4</mn></mrow></math> supersymmetric Yang-Mills charged plasma in <math altimg='si3.svg'><msup><mrow><mi mathvariant='double-struck'>R</mi></mrow><mn>3</mn></msup></math> with equal chemical potentials for the maximal Abelian subgroup of the <italic>R</italic>-symmetry group become dynamically unstable below some critical temperature. The instabilities arise in the <italic>R</italic>-symmetry charge transport, precisely when the equilibrium state becomes thermodynamically unstable. We study the fate these correlated instabilities when the theory is placed on <italic>S</italic> 3. The curvature of the three-sphere affects the onset of the dynamical and the thermodynamic instabilities differently: increasing the curvature at low temperatures can stabilize its transport, but leave the plasma thermodynamically unstable. Thermodynamic stability is never recovered provided the <italic>S</italic> 3 volume is allowed to fluctuate. <math altimg='si2.svg'><mrow><mi mathvariant='script'>N</mi><mo linebreak='goodbreak'>=</mo><mn>4</mn></mrow></math> SYM is always thermodynamically unstable in the fixed-pressure ensemble on <italic>S</italic> 3 as well.

Canada

Alex Buchel

Instability in <math altimg='si2.svg'><mrow><mi mathvariant='script'>N</mi><mo linebreak='goodbreak'>=</mo><mn>4</mn></mrow></math> supersymmetric Yang-Mills theory on <italic>S</italic> 3 at finite density

We investigate the discovery potential of the $T_{bc}$ state with $J^P = 0^+$ in proton-proton ( $pp$ ) collisions at LHCb at a center-of-mass energy of $\sqrt{s} = 13~{\rm{TeV}}$ . The study focuses on the decay channel $T_{bc} \to B^- D^+$ . A phenomenological approach is employed to construct the background model based on the associated production of $\textit{B}$ and $\textit{D}$ mesons, incorporating previously published LHCb results. Background processes are simulated using ${\mathtt{MadGraph5\_aMC@NLO}}$ and ${\mathtt{Pythia8.3}}$ . We explore the parameter space of the $T_{bc}$ mass, width, production cross section, and the effective double-parton scattering cross section ( $\sigma_{{\rm{eff}}}$ ) relevant for the $B D$ meson background. The integrated luminosity required for a $5\sigma$ discovery at LHCb is evaluated under various assumptions. In particular, we consider three representative $T_{bc}$ production cross section scenarios: an optimistic estimate of $103~{\rm{nb}}$ , an intermediate value of $18~{\rm{nb}}$ obtained by scaling from the $T_{cc}^+$ production cross section, and a conservative lower bound of $0.3~{\rm{nb}}$ . We find that a $5\sigma$ observation is achievable for a production cross section of $103~{\rm{nb}}$ , which is expected to be within reach during Run4. In contrast, the more realistic cross section estimate of $18~{\rm{nb}}$ requires the full Run5 dataset ( $300~{\rm{fb}}^{-1}$ ) under the most favorable parameter choices. For the conservative scenario, no significant signal would be observable even with $300~{\rm{fb}}^{-1}$ . In addition, we estimate the minimum observable $\sigma(T_{bc}) \times {\cal{B}}(T_{bc} \to $ $ B^- D^+)$ for a $5\sigma$ discovery under different luminosity scenarios, providing guidance for future experimental searches at LHCb.

Mingjie Feng

Yiming Li

France

Hua-Sheng Shao

Prospects for discovering strongly decaying doubly heavy T$_{bc}$ tetraquark states at LHCb * Mingjie Feng and Yiming Li is Supported by the National Natural Science Foundation of China (NSFC) (2175245, 12188102, W2443008). Hua-Sheng Shao is Supported by the European Research Council (101041109, 'BOSON') and the French National Research Agency (grant ANR-20-CE31-0015, 'PrecisOnium')

Building upon the algebraic consistency construction of one-loop Bern-Carrasco-Johansson (BCJ) numerators for Yang-Mills (YM) and Yang-Mills-scalar (YMS) theories, we explore the expansion formula of one-loop Einstein-Yang-Mills (EYM) integrands (with a gluon loop) in terms of conventional one-loop YM integrands with quadratic propagators. We first express the EYM integrand by tree-level amplitudes according to the forward limit approach. Employing a two-step expansion strategy, the gluon-loop EYM integrand is decomposed into tree-level YM amplitudes under the forward limit, which are subsequently expanded into tree-level bi-adjoint scalar (BS) ones. We then prove that when the kinematic coefficients in both expansion steps satisfy the one-loop consistency conditions, the EYM integrand is finally expanded as a combination of YM integrands with quadratic propagators. The coefficients in this expansion formula coincide exactly with those in the expansion formula for YMS integrands. This correspondence highlights a shared kinematic structure, providing the proper foundation for constructing BCJ numerators in both YMS and EYM theories at one loop.

Yi-Jian Du

Chongsi Xie

Expansion formula of one-loop Einstein-Yang-Mills integrand