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.

China

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

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

We employ the harmonic superspace methods to study a six-dimensional 𝒩 = (1$\textit{,}$ 0) supersymmetric gauge theory with higher derivatives coupled to a hypermultiplet in the adjoint representation. By introducing a certain non-minimal interaction between the gauge multiplet and the hypermultiplet, we demonstrate that the one-loop divergences in gauge superfield sector, which are present in the conventional formulation, are canceled. The resulting theory is off-shell one-loop finite in this sector, while preserving the gauge invariance and 𝒩 = (1$\textit{,}$ 0) supersymmetry. The cancelation mechanism is explicitly verified using both the background field method and the supergraph techniques. Thus, we present an example of the higher-derivative supersymmetric gauge theory in six dimensions which is finite in the vector multiplet sector.

Russia

I. Buchbinder

A. Budekhina

E. Ivanov

K. Stepanyantz

One-loop finiteness in higher-derivative 6$\textit{D}$, 𝒩 = (1, 0) super Yang-Mills — hypermultiplet system

We calculate the resummed perturbative free energy of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">N</mi><mo>=</mo><mn>4</mn></math> supersymmetric Yang-Mills in four spacetime dimensions (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>SYM</mi></mrow><mrow><mn>44</mn></mrow></msub></mrow></math>) to order <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>λ</mi><mrow><mn>5</mn><mo>/</mo><mn>2</mn></mrow></msup></math> in the ‘t Hooft coupling at finite temperature and zero chemical potential. All infrared divergences cancel when we include contributions from <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>SYM</mi></mrow><mrow><mn>44</mn></mrow></msub></mrow></math> ring diagrams and the final result is both ultraviolet and infrared finite. Our result has special significance since order <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>λ</mi><mrow><mn>5</mn><mo>/</mo><mn>2</mn></mrow></msup></math> is the highest order calculation that can be done with perturbation theory, because there are nonperturbative effects associated with the magnetic mass scale that come into play at order <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>λ</mi><mn>3</mn></msup></math>. We compare results obtained with regularization by dimensional reduction (RDR), which preserves supersymmetry, and canonical dimensional regularization (DR). We also compare with a generalized Padé approximant constructed by matching the weak coupling result at order <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>λ</mi><mn>2</mn></msup></math> and the large <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>c</mi></msub></math> strong coupling result at order <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>λ</mi><mrow><mo>−</mo><mn>3</mn><mo>/</mo><mn>2</mn></mrow></msup></math>. Finally we make a comparison between our result and the QCD free energy and show that <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>SYM</mi></mrow><mrow><mn>44</mn></mrow></msub></mrow></math> has better convergence properties.

Margaret E. Carrington

Gabor Kunstatter

Saudi Arabia

Ubaid Tantary

<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">N</mi><mo>=</mo><mn>4</mn></mrow></math> supersymmetric Yang-Mills thermodynamics to order <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>λ</mi><mrow><mn>5</mn><mo>/</mo><mn>2</mn></mrow></msup></math>