The one-loop gravitational path integral around Euclidean de Sitter space $\textit{S}$ has a complex phase that casts doubt on a state counting interpretation. Recently, it was proposed to cancel this phase by including an observer. We explore this proposal in the case where the observer is a charged black hole in equilibrium with the de Sitter horizon. We compute the phase of the one-loop determinant within a two-dimensional dilaton gravity reduction, using both numerical and analytical methods. Our results interpolate between previous studies of a probe geodesic observer and the Nariai solution. We also revisit the prescription for going from the Euclidean path integral to the state-counting partition function, finding a positive sign in the final density of states.

United States

Yiming Chen

Douglas Stanford

Haifeng Tang

China

Zhenbin Yang

On the phase of the de Sitter density of states

Elliptic de Sitter (dS) spacetime dS/$\textit{ℤ}$ is a non-time-orientable spacetime obtained by imposing an antipodal identification to global dS. Unlike QFT on global dS, whose vacuum state can be prepared by a no-boundary Euclidean path integral, the Euclidean elliptic dS does not define a wavefunction in the usual sense. We propose instead that the path integral on the Euclidean elliptic dS defines a no-boundary density matrix. As an explicit example, we study the free Dirac fermion CFT in two-dimensional elliptic dS and analytically compute the von Neumann and the Rényi entropies of this density matrix. The calculation reduces to correlation functions of vertex operators on non-orientable surfaces. As a by-product, we compute the time evolution of entanglement entropy following a crosscap quench in free Dirac fermion CFT. We also comment on a striking feature of free QFT in elliptic dS: its global Hilbert space is one-dimensional, wheres the Hilbert space associated to each observer is a nontrivial Fock space.

France

Raphaël Dulac

Zixia Wei

No boundary density matrix in elliptic de Sitter dS/$\textit{ℤ}$ 2

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.

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)

Modular invariance is a fundamental symmetry in string compactifications, constraining both the structure of the effective theory and the dynamics of moduli and matter fields. It has also gained renewed importance in the context of swampland conjectures and, independently, flavour physics. We investigate a modular-invariant scalar potential arising from heterotic orbifolds, where the flavour structure and moduli dynamics are jointly shaped by the underlying geometry. Focusing on a string-inspired, two-moduli truncation, we uncover a rich vacuum structure featuring anti-de Sitter minima and unstable de Sitter saddle points. We identify large regions in moduli space supporting multifield hilltop quintessence consistent with observations. All solutions satisfy refined swampland de Sitter bounds. Our results illustrate how modular symmetry can guide the construction of controlled, string-motivated quintessence scenarios within consistent effective theories.

Mexico

Hansel Gordillo-Ruiz

Miguel Hernández-Segura

Ignacio Portillo-Castillo

Saúl Ramos-Sánchez

United Kingdom

Ivonne Zavala

Rolling with modular symmetry: quintessence and de Sitter in heterotic orbifolds

This paper is devoted to study the thermodynamics of charged de Sitter black holes in Einstein–Bumblebee gravity, a Lorentz-violating extension of general relativity, using an effective two-horizon framework that treats the region between the event and cosmological horizons as a single thermodynamic system. We derive globally consistent thermodynamic variables such as effective temperature, pressure, and volume and show that they satisfy a generalized first law. The effective heat capacity shows a strong Schottky-type anomaly, which is defined by a single-peak structure resulting from the interaction between the two horizons. It is demonstrated here that Lorentz-violating effects cause this feature to undergo systematic and controlled deformations. In particular, we observe that the Lorentz-violation parameter leads to a displacement and rescaling of the heat-capacity peak, which can be interpreted as a change of the effective excitation scale for the thermodynamic response. We also show that the overall thermodynamics of the two-horizon system can be effectively described by a phenomenological finite-level model, where the temperature difference between the horizons acts as an effective excitation gap. Although the map is not derived microscopically, it accurately reproduces the shape of the heat-capacity curve and allows one to interpret the macroscopic thermodynamical enhancement. Our results reveal that Lorentz-violating corrections act like a controlled change to the thermodynamics of black holes with multiple horizons. They keep the overall Schottky-type pattern but change the specific numerical details. This highlights the strong sensitivity of horizon thermodynamics to corrections beyond standard gravity and provides a systematic approach to study these deviations within a semiclassical framework.

Saudi Arabia

Nazek Alessa

Pakistan

Azerbaijan

M. Umair Shahzad

Anees Ashfaq

Discrete microstate spectra and Schottky anomaly in charged de Sitter black holes via bumblebee gravity

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

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