Within the framework of Dyson-Schwinger equations (DSEs) and by means of the Multiple Reflection Expansion approximation, we study the finite volume effects on the constituent quark mass in a strong external magnetic field. Since the magnetic field influences the coupling constant, which controls the strength of strong interactions in QCD, we adopt the magnetic-field-dependent running coupling constant in our simulations. The results show that, in addition to the magnetic field, the masses of constituent quarks also have a significant dependence on the volume and the running coupling constant. The model behaves closely to the infinite volume limit for large sizes, but the effect of the finite volume is significant when the system size $\textit{R}$ is about $ 2-6 $ fm. The finite volume effects and the magnetic-field-dependent running coupling constant have considerable influence on the phase transition.

China

Li-Juan Zhou

De-Xian Wei

Zhong-Yi Liu

Hong-Wei Zhong

Dynamical quark mass and finite volume effects in the Dyson-Schwinger equations * Li-Juan Zhou has been supported by the National Natural Science Foundation of China (11865005), the Natural Science Foundation of Guangxi (China) (2025GXNSFAA069552). De-Xian Wei has been supported by the National Natural Science Foundation of China (12105057), the Natural Science Foundation of Guangxi (China) (2023GXNSFAA026020)

We study the evolution of charged, asymptotically de Sitter black holes close to the cold extremal branch of the phase space. We consider black hole sizes that are parametrically smaller than both their inverse temperature and the cosmological horizon. Unlike flat space, charged de Sitter black holes do not evolve towards extremality, but rather towards a thermal equilibrium with the cosmological horizon. In the low-temperature regime, the near-horizon physics can be effectively captured by a one-dimensional Schwarzian theory. This is coupled to the far-horizon de Sitter quantum field theory. Incorporating the thermal nature of the cosmological horizon, we compute the quantum energy transfer through uncharged massless scalar particles. The results significantly differ from Hawking’s thermal predictions. Black holes that are hotter than the cosmological horizon emit energy at a rate lower than their asymptotically flat counterparts. Whereas much colder ones absorb energy at a nearly constant rate.

Poland

Arindam Bhattacharjee

India

Muktajyoti Saha

Quantum evolution of de Sitter black holes near extremality

This work is motivated by the recent evidence for a double-copy relationship between open- and closed-string amplitudes in Anti-de Sitter (AdS) space. At present, the evidence has the form of a double-copy relation for string-amplitude building blocks, which are combined using the multiple-polylogarithm (MPL) generating functions. These generate MPLs relevant for all-order AdS curvature corrections of four-point string amplitudes. In this paper, we prove this building-block double copy using a new, noncommutative version of twisted de Rham theory. In flat space, the usual twisted de Rham theory is already known to be a natural framework to describe the Kawai-Lewellen-Tye (KLT) double-copy map from open- to closed-string amplitudes, in which the KLT kernel can be computed from the intersections of the open-string amplitude integration contours. We formulate twisted de Rham theory for noncommutative-ring-valued differential forms on complex manifolds and use it to derive the intersection number of two open-string contours, which are closed in the noncommutative twisted homology sense. The inverse of this intersection number is precisely the AdS double-copy kernel for the four-point open- and closed-string generating functions.

Hiren Kakkad

Alexander Ochirov

Shijie Zhang

Twisted de Rham theory for string double copy in AdS

Generic solutions are studied in Einstein-scalar gravity in an ansatz that can interpolate between de Sitter and Anti-de Sitter regimes. The scalar potential is arbitrary. All solutions are determined by their end-points in the scalar field space. All such end-points are classified. This provides a complete classification and characterization of the full space of regular solutions. It is shown that there are no regular (Centaur) solutions that interpolate between an AdS boundary and a dS interior, within our ansatz, when $\textit{d >}$ 2. This no-go theorem persists in the presence of multiple scalar fields with a non-trivial field space metric. The Gubser classification of regular solutions is also upgraded to include cases that are not Lorentz invariant and do not contain AdS boundaries.

Greece

France

Elias Kiritsis

Romania

Sergio Morales-Tejera

Christopher Rosen

de Sitter versus Anti de Sitter flows and the (super)gravity landscape. Part II

We establish a no-go theorem in the context of string and M-theory flux compactifications on Riemann-Flat manifolds with Casimir energy. Specifically, we show that no dS minimum exists in this setup in dimension $\textit{d}$ > 3. The case of dS minima is not excluded, but their actual fate can only be ascertained via an explicit construction. We also point out that the problem of finding dS minima on RFM’s and more general flux compactifications is mathematically equivalent to a semidefinite programming problem, identical to those studied in CFT bootstrap, and hence the search for dS can benefit from the existing vast literature and numerical tools. We illustrate this in a toy model.

Spain

Bruno Bento

Miguel Montero

de Sitter no-go’s for Riemann-flat manifolds and a link to semidefinite optimisation

One-loop <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>S</mi><mrow><mi>d</mi><mo>+</mo><mn>1</mn></mrow></msup></math> path integrals were shown to factorize into two parts: a bulk thermal ideal gas partition function in a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>d</mi><msub><mi>S</mi><mrow><mi>d</mi><mo>+</mo><mn>1</mn></mrow></msub></math> static patch and an edge partition function associated with degrees of freedom living on <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>S</mi><mrow><mi>d</mi><mo>−</mo><mn>1</mn></mrow></msup></math>. Here, we analyze the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="fraktur">so</mi><mo stretchy="false">(</mo><mi>d</mi><mo stretchy="false">)</mo></math> structure of the edge partition functions for massive and massless totally symmetric tensors of arbitrary rank in any <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>d</mi><mo>≥</mo><mn>3</mn></math>. For linearized Einstein gravity on <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>S</mi><mrow><mi>d</mi><mo>+</mo><mn>1</mn></mrow></msup></math>, we find that the edge partition function receives contributions from shift-symmetric vector and scalar fields on <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>S</mi><mrow><mi>d</mi><mo>−</mo><mn>1</mn></mrow></msup></math>, suggesting a possible interpretation in terms of an embedded <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>S</mi><mrow><mi>d</mi><mo>−</mo><mn>1</mn></mrow></msup></math> brane.

Y.T. Albert Law

de Sitter horizon edge partition functions

We discuss the symmetry aspects of quantum field theory in global four-dimensional de Sitter spacetime linked to SO(1, 4) isometries. For the unitary irreducible representations relevant to elementary particles, we obtain explicit transformation laws for the symmetry generators acting on one-particle states in a basis adapted to the SU(2) × SU(2) decomposition of the Hilbert space. Using these results, we derive the corresponding Ward identities and demonstrate how global spacetime symmetries constrain de Sitter scattering amplitudes. We show that the Poincaré algebra and flat-space Ward identities are recovered in the large-momentum limit.

United States

Audrey Lindsay

Tomasz Taylor

Symmetries of de Sitter particles and amplitudes

We present a fully analytic treatment of Schwarzschild–de Sitter (SdS) black-hole evaporation in two-dimensional dilaton gravity with anomaly-induced backreaction. Starting from the spherical reduction of four-dimensional Einstein gravity with a cosmological constant, we construct an exactly solvable 2D model that captures the full causal and thermodynamic structure of the SdS static patch, including both black-hole and cosmological horizons. Incorporating the trace anomaly of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math> conformal matter fields via the Polyakov action, we determine the evolution of the black-hole mass and geometry in the Unruh–de Sitter state, track the steady nonequilibrium Hawking flux, and compute local thermodynamic observables for static observers. The conserved Killing energy flux drives an irreversible heat current from the black hole to the cosmological horizon whenever their surface gravities differ, ensuring monotonic entropy growth and satisfaction of the generalized second law. We prove that <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>κ</mi><mi>b</mi></msub><mo>&gt;</mo><msub><mi>κ</mi><mi>c</mi></msub></math> throughout the physical static patch, so the only zero-flux configuration is the Nariai limit where the horizons coincide. Extending the framework to the quantum-information regime, we construct a thermo-controlled estimate of the Page curve and show how quantum extremal surfaces and entanglement islands emerge naturally within the anomaly-induced steady state. These results constitute a fully analytic, backreacted solution for SdS evaporation that unifies semiclassical thermodynamics and information flow in a cosmological setting, thereby elucidating the ultimate fate of evaporating black holes in de Sitter space.

Damien A. Easson

Fate of Schwarzschild–de Sitter black holes: Nonequilibrium evaporation

In this work, we initiate the study of light-ray operators in four-dimensional de Sitter space focusing on null integrals of the stress tensor. In Minkowski space, the null integral of the stress tensor unifies several ostensibly different constructions, functioning simultaneously as the energy flux operator, the angular contribution to a conserved charge, the averaged null energy operator, and the light transform of the stress tensor. However, we show that the de Sitter analogs of these various interpretations do not necessarily coincide but rather lead to distinct, observer-dependent light-ray operators. We construct four such de Sitter analogs and analyze their matrix elements in a free, conformally coupled scalar theory, showing that they exhibit the expected symmetry and positivity properties.

Shounak De

Yakov Landau

De Sitter light-ray operators

We study nonequilibrium initial states of quantum fields in curved spacetime and develop a framework for describing global quenches as unitary perturbations of the initial density matrix. Using the Keldysh-Schwinger functional integral, we derive expressions for postquench correlators in arbitrary geometries and apply the method to both Minkowski and de Sitter backgrounds. In flat space, the approach reproduces the known relaxation behavior for massive fields and reveals qualitatively distinct dynamics in the massless case. In de Sitter space, we find that the late-time decay of quench-induced corrections depends sensitively on the mass and may influence the behavior of cosmological observables such as the power spectrum. The framework also extends straightforwardly to non-Gaussian initial states, providing a basis for future studies of loop effects and primordial non-Gaussianities.

Ivan A. Belkovich

Damir Sadekov

Gleb S. Zverev

Global quenches and correlator dynamics in de Sitter space