<p>We investigate the QCD phase diagram and the associated Lee–Yang edge singularities using the two-flavor nonlocal Nambu–Jona-Lasinio model extended to complex chemical potential. We show explicitly there exists a strong correlation between the chiral phase transition and the patterns in the effective potential in the complex plane of order parameter, serving as a criterion to differentiate crossover from first-order transitions. Typically, the Lee–Yang edge singularities can be understood as a generalization of the critical end point (CEP) separating the crossover and the first-order transition, where the positive Nambu phase and the Wigner phase coalesce. We further analyze the scaling behavior near the CEP by extracting the critical exponent associated with the Lee–Yang singularities. Additionally, we confirm that the extrapolation of the Lee–Yang edge singularity trajectories provides an efficient method of determining the CEP location, even at a small real chemical potential. This provides a viable method for exploring regions of the QCD phase diagram that remain inaccessible to lattice QCD.</p>

Zong-shuai Zhang

Yi Lu

Yu-xin Liu

Lee-Yang edge singularities in a nonlocal Nambu–Jona-Lasinio model

It is known that Yang-Mills theories, especially in the large-$\textit{N}$ limit, exhibit a $\textit{θ}$-vacuum structure with a multi-branched vacuum energy. In this work, we demonstrate that this multi-branch structure can play a crucial role in axion cosmology when the axion acquires its mass from the Yang-Mills sector, even when that sector is never reheated by the inflaton. The key observation is that the axion potential is directly tied to the tunneling rate between adjacent branches. We find qualitatively new phenomena, including a new class of first-order phase transitions, bouncing bubbles, and nested “bubbles-within-bubbles”. When the axion has a decay constant around the Planck scale, as motivated by the string Axiverse, the axion can be driven near the hilltop by inflationary dynamics, allowing the phase transition to be triggered. The associated energy release can be large enough to generate a significant stochastic gravitational-wave background, produce primordial black holes, or populate the Yang-Mills sector with particles. These phenomena represent novel predictions of the Axiverse and should be taken into account when assessing the cosmological impact of axions or axion-like particles. To recover conventional axion cosmology, one must suppress or avoid the dynamics discussed in this work.

Japan

Tsubasa Sugeno

Wen Yin

Axion cosmology with multi-branch Yang-Mills

In this work, we consider a spherically symmetric static black hole metric in Kalb–Ramond (KR) gravity, and investigate the impact of relevant parameters on the black hole shadow and polarization images. For black hole shadow images, we consider two geometrically thick accretion disk models such as a phenomenological RIAF-like model and an analytical BAAF disk model. In each case, we observe a bright ring-like structure corresponding to the higher-order images with a surrounding region of non-zero intensity that represents the primary image. The increasing values of $$\hat{\lambda }$$ or $$\hat{\gamma }$$ results in decrease the size of the higher-order image, while increasing values of observer inclination $$\theta _{o}$$ alter its shape and cause the horizons outline to be obscured. On the other hand, in BAAF disk model, at high observer inclinations, the obscuration of the horizons outline by radiation from outside the equatorial plane is weakened. Consequently, the brightness of the primary image in the phenomenological model is significantly greater than that in the BAAF disk model, indicating the strong gravitational lensing effect. For the polarized images, we use only the BAAF disk model with anisotropic radiation, assuming an infalling accretion flow matter. The obtained results illustrate that the polarization intensity $$P_{o}$$ in the higher-order image region is significantly stronger than as compare to other regions, and it is rapidly decreases away from this region. The variation in $$\hat{\lambda }$$ and $$\hat{\gamma }$$ depicts the intrinsic structure of the space-time and $$\theta _o$$ depends on the observers orientation, together they shape the polarization features.

China

Xiao-Xiong Zeng

Chen-Yu Yang

Pakistan

Muhammad Aslam

Rabia Saleem

Probing non-rotating black hole in Kalb–Ramond gravity: imaging and polarized signatures surrounded by different thick accretion flows

We propose a SymTFT for 4d U($\textit{N}$) Yang-Mills theory and its variants. We show that the SymTFT reproduces the structure of the global one-form symmetry in these theories. We consider the holographic embedding of this SymTFT, and observe that SymTFT’s containing continuous symmetries are not always obtained as a near boundary limit of the supergravity action.

Israel

United States

Oren Bergman

Italy

Eduardo Garcia-Valdecasas

Spain

Francesco Mignosa

Diego Rodriguez-Gomez

The SymTFT of $\textit{u}$($\textit{N}$) Yang-Mills Theory and holography

The dynamics of Wilson loops are governed by an infinite set of Schwinger-Dyson equations and trace relations. In the context of the lattice positivity bootstrap, a central challenge is determining a dynamically independent basis of these operators within a truncated space. We present a systematic framework to address this problem, utilizing a geometric plaquette-cut and subloop-cut strategy to efficiently generate all (local) direct equations. Furthermore, we identify and analyze “indirect equations”, which arise from the elimination of higher-length intermediate loops. We elucidate the origin of these subtle relations and propose a vertex-filtering strategy to construct them. Applying the above framework to SU(2) lattice Yang-Mills theory, we provide explicit counts of independent canonical loops and equations in 2, 3, and 4 dimensions, along with a statistical analysis of their asymptotic growth.

Xizhe Liu

Gang Yang

Direct and indirect loop equations in lattice Yang-Mills theory

Using ray-tracing techniques, this paper investigates the optical and polarization images of rotating black holes in Kalb–Ramond (KR) gravity illuminated by thick accretion disks. We examine two accretion disk models: the phenomenological radiatively inefficient accretion flow (RIAF) model and the analytical ballistic approximation accretion flow (BAAF) model. The RIAF model incorporates both isotropic and anisotropic radiation. In all models, external bright rings corresponding to high-order images and an internal dark region associated with the event horizon are observed. At high observational inclinations, the inner shadow is obscured by radiation from the equatorial plane, which is significantly different from the thin accretion disk model. The primary distinction between isotropic and anisotropic radiation is that the latter causes distortion of the high-order image in the vertical direction, resulting in an elliptical structure. For the BAAF model, because certain regions become geometrically thinner under the conical approximation, the high-order images are narrower compared to those in the RIAF model. Furthermore, we find that an increase in the rotational parameter $\textit{a}$ leads to asymmetry in the intensity distribution of the high-order image, while an increase in the spontaneous Lorentz-violating parameters, $$\varsigma $$ and $$\varpi $$ , results in a decrease in the size of the high-order image. In the polarization image, linear polarization is found to be significantly influenced by the intensity, while it is relatively less affected by the parameters $$\varsigma $$ and $$\varpi $$ . The electric vector position angle is mainly affected by the parameters $$\varsigma $$ and $$\varpi $$ .

Huan Ye

Shadow and polarization images of rotating black holes in Kalb–Ramond gravity illuminated by several thick accretion disks

In this paper, we derive characteristic identities for the split Casimir operator of the Lie algebra <italic>so</italic> <inf>2<italic>r</italic></inf> in tensor products of spinor representations of the same and opposite chiralities. Using these identities, we explicitly construct projectors onto invariant subspaces of this operator and compute their traces. The results obtained allow us to derive explicit expressions for the colour factors of ladder Feynman diagrams in gauge theories with gauge group Spin(2 <italic>r</italic>).In addition, we obtain a new form of a solution to the Yang-Baxter equation that is invariant under the action of the Lie algebra <italic>so</italic> <inf>2<italic>r</italic></inf> in spinor representations.

Russia

A.P. Isaev

A.A. Provorov

Split Casimir operator of the Lie algebra <italic>so</italic> <inf>2<italic>r</italic></inf> in spinor representations, colour factors, and the Yang-Baxter equation

<p>We set the scale of <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 theories for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi><mo>=</mo><mn>3</mn></math>, 5, 8 and in the large-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math> limit via gradient flow, as a first step towards the computation of the large-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math> <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Λ</mi></math>-parameter using step scaling. We adopt twisted boundary conditions to achieve large-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math> volume reduction and the Parallel Tempering on Boundary Conditions algorithm to tame topological freezing. This setup allows accurate determinations of the gradient-flow scales down to lattice spacings as fine as <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>∼</mo><mn>0.025</mn><mtext> </mtext><mtext> </mtext><mi>fm</mi></math> for all the explored values of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math>, a regime that has never been reached with ergodic algorithms. Moreover, we are able to precisely estimate the finite-size systematics related to topological freezing, and to show the suppression of finite-volume effects expected by virtue of large-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math> twisted volume reduction.</p>

Claudio Bonanno

Jorge Luis Dasilva Golán

Margarita García Pérez

Massimo D’Elia

Andrea Giorgieri

Scale setting of <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 theory, topology and large-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math> volume independence

We investigate the dynamics of four-dimensional $$ \mathcal{N}=2 $$ SU(2) super Yang-Mills theory on an AdS background. We propose that the boundary conditions that preserve the AdS super-isometries are determined by maximizing the real part of the AdS partition function $\textit{F}$ = −log $\textit{Z}$ . At weak coupling Λ$\textit{L}$ ≪ 1 the maximization singles out the Dirichlet boundary condition with an SU(2) boundary global symmetry, corresponding to the classical vacuum at the origin of the Coulomb branch with fully un-higgsed gauge group. We find that for Λ$\textit{L}$ ~ 𝒪(1) new boundary conditions are favored, with gauge-group higgsed down to U(1), matching the expectation from the flat space limit. We use supersymmetric localization to compute $\textit{Z}$ nonperturbatively. We further provide evidence for a relation between $\textit{F}$ and the $$ \mathcal{N}=2 $$ prepotential in AdS background.

Davide Bason

United Kingdom

Christian Copetti

Lorenzo Pietro

Ziming Ji

$$ \mathcal{N}=2 $$ super Yang-Mills in AdS4 and $\textit{F}$ AdS-maximization

We systematically classify all supersymmetry-preserving mass deformations of SYM matrix models in all dimensions ($\textit{D}$ = 3, 4, 6, 10). In $\textit{D}$ = 10, the polarized IKKT model emerges as the only possible deformation. In $\textit{D}$ = 4, we identify two massive models without a sign problem, making them attractive candidates for non-perturbative numerical studies.

Switzerland

Adrien Martina

Massive deformations of supersymmetric Yang-Mills matrix models