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)

A correction to this paper has been published: https://doi.org/10.1007/JHEP04(2025)171

United States

Molly Kaplan

Donald Marolf

Xuyang Yu

Ying Zhao

Erratum to: De Sitter quantum gravity and the emergence of local algebras

Recently, references [1, 2] found that the repetitive Penrose process cannot extract all the extractable rotational energy of a Kerr black hole, and reference [3] found that the repetitive electric Penrose process cannot extract all the electrical energy of a Reissner-Nordström (RN) black hole. In this paper, we intend to study the repetitive Penrose process in the Kerr-de Sitter (Kerr-dS) black hole. We will explore influences of the cosmological parameter on the repetitive Penrose process. The results show that, apart from the comparable features documented earlier, the Kerr-dS black hole yields a higher energy return on investment (EROI) and single-extraction energy capability compared to the Kerr black hole. Specifically, the larger the cosmological parameter, the stronger the EROI and the single-extraction energy capability. Furthermore, we also find that at a lower decay radius, the Kerr black hole exhibits a higher energy utilization efficiency (EUE) and more extracted energy after the repetitive Penrose process is completed. However, at a higher decay radius, the situation is reversed, i.e., the Kerr-dS black hole exhibits a higher EUE and more extracted energy, which is due to the existence of stopping condition of the iteration.

Ke Wang

Xiao-Xiong Zeng

Repetitive Penrose process in Kerr-de Sitter black holes

We investigate gauge dependence of one-graviton-loop corrections to the effective field equation of the massless, minimally coupled scalar in de Sitter, obtained by including source and observer corrections to the effective self-mass correcting the equation. Using the ∆$\textit{α}$ variation of the de Sitter-breaking graviton propagator in a one-parameter family of gauges, we compute the gauge-dependent contributions to the effective self-mass of a massless minimally coupled scalar mediating interactions between heavy scalars. We show that gauge dependence cancels provided the contributions from all diagram classes are collected, including one-loop corrections to external mode functions, which play a qualitatively new role relative to flat space. The resulting cancellation supports the construction of graviton gauge-independent cosmological quantum-gravitational observables from quantum-corrected effective equations.

Czechia

Dražen Glavan

Taiwan

Shun-Pei Miao

Netherlands

Tomislav Prokopec

Richard Woodard

Cancellation of one-parameter graviton gauge dependence in the effective scalar field equation in de Sitter

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

<p>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.</p>

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.

Audrey Lindsay

Tomasz Taylor

Symmetries of de Sitter particles and amplitudes