We compute a gravitational on-shell action of a finite, spherically symmetric causal diamond in ($\textit{d}$ + 2)-dimensional Minkowski spacetime, finding it is proportional to the area of the bifurcate horizon $$ {A}_{\mathcal{B}} $$ . We then identify the on-shell action with the saddle point of the Euclidean gravitational path integral, which is naturally interpreted as a partition function. This partition function is thermal with respect to a modular Hamiltonian $\textit{K}$. Consequently, we determine, from the on-shell action using standard thermodynamic identities, both the mean and variance of the modular Hamiltonian, finding 〈$\textit{K}$〉 = 〈(∆$\textit{K}$) 〉 = $$ \frac{A_{\mathcal{B}}}{4{G}_N} $$ . Finally, we show that modular fluctuations give rise to fluctuations in the geometry, and compute the associated phase shift of massless particles traversing the diamond under such fluctuations.

United States

Kwinten Fransen

Temple He

Kathryn Zurek

Thermodynamics of a spherically symmetric causal diamond in Minkowski spacetime

Inspired by the novel idea proposed by Padmanabhan [<a href="http://dx.doi.org/10.1103/PhysRevD.100.045024">Phys. Rev. D 100, 045024 (2019)</a>], we develop a method to uncover the hidden thermal properties of the inertial Feynman propagator in Minkowski spacetime in a causally consistent manner. This, in turn, enables a coherent interpretation based on future-directed propagation. In our approach, the Fourier transform is implemented following the convention used in the analysis of vacuum fluctuations. As a result, future-directed propagation across causal horizons can be consistently interpreted, from the perspective of an observer confined to a causally disconnected region, as the emission of scalar quanta at the past horizon and their absorption at the future horizon. Moreover, we find that the ratio between emission and absorption processes reproduces the characteristic Boltzmann factor of a thermal ensemble. We first apply this analysis to a causal diamond of length <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>2</mn><mi>α</mi></math>, performing a detailed study of the near-horizon geometry and thereby obtaining the temperature associated with the thermal behavior of the Minkowski vacuum as perceived by an observer with finite lifetime <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>2</mn><mi>α</mi></math>. For completeness, we also apply the method to the right Rindler wedge, recovering the well-known Unruh temperature, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>T</mi><mo>=</mo><mi>a</mi><mo>/</mo><mo stretchy="false">(</mo><mn>2</mn><mi>π</mi><mo stretchy="false">)</mo></math>. Our results demonstrate that thermality can emerge directly from causal structure, independently of acceleration or gravity, with causal diamonds encoding intrinsic thermodynamic behavior in quantum field theory.

Nada Eissa

Carlos R. Ordóñez

Gustavo Valdivia-Mera

Thermal nature of the causal diamond horizon: A hidden property of the inertial propagator

In this article, we extend the horizon brightened acceleration radiation (HBAR) framework, originally introduced by Marlan Scully et al. in [Proceedings of the National Academy of Sciences Vol. 115, pp. 8131 (2018)], to the causal diamond (CD) spacetime. We study a cloud of two-level atoms, injected at random times in the asymptotic past of the CD, freely falling toward its causal horizon and emitting scalar radiation via a weak dipole coupling to a quantum field. In the near-horizon region, an emergent conformal symmetry—captured by conformal quantum mechanics (CQM)—governs the field dynamics and allows analytic control of the emission process. We find that the radiation spectrum is thermal, with temperature <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mi>D</mi></msub><mo>=</mo><mn>1</mn><mo>/</mo><mo stretchy="false">(</mo><mi>π</mi><mi>α</mi><mo stretchy="false">)</mo></math>, and that the associated von Neumann entropy flux reproduces the entropy production of the radiation field. These results demonstrate that the causal horizons of the CD spacetime effectively act as a topological thermal reservoir, with thermal properties arising entirely from the global causal structure rather than from underlying microscopic degrees of freedom, highlighting that the validity of the HBAR framework is fundamentally tied to the existence of causal horizons, independent of the presence of a black hole.

Horizon brightened acceleration radiation entropy in causal diamond geometry: A near-horizon perspective

A comprehensive study integrating the microscopic structure of spacetime and the principle of quantum superposition is capable of offering a fundamental bottom-up approach for understanding the quantum aspect of gravity. In this paper, we present a framework for the superposition of spacetime structures in the causal diamond spacetime and analyze the behavior of quantum entanglement generated by spacetime superposition from the perspective of relativistic quantum information. For the first time, we combine the concept of spacetime superposition with causal diamonds and derive the analytical expression of the Unruh-diamond vacuum state for Dirac fields in the causal diamond spacetime. Based on this, we analyze both initially correlated and uncorrelated modes in superposed and classical causal diamond spacetimes, and quantifying how quantum thermal effects arising from spacetime structure alter entanglement. Our findings reveal that quantum entanglement degrades in classical diamond spacetime, while the superposed structure generates additional entanglement resources between modes in superposed diamond spacetimes. From a quantum information perspective, our results suggest that the characteristics of spacetime structural manifestations can serve as valuable resources for performing quantum information processing tasks.

China

Xiaofang Liu

Changjing Zeng

Jieci Wang

Generation of quantum entanglement in superposed diamond spacetime

We present a method to directly detect the axion dark matter using nitrogen vacancy centers in diamonds. In particular, we use metrology leveraging the nuclear spin of nitrogen to detect axion-nucleus couplings. This is achieved through protocols designed for dark matter searches, which introduce a novel approach of quantum sensing techniques based on the nitrogen vacancy center. Although the coupling strength of the magnetic fields with nuclear spins is three orders of magnitude smaller than that with electron spins for conventional magnetometry, the axion interaction strength with nuclear spins is the same order of magnitude as that with electron spins. Furthermore, we can take advantage of the long coherence time by using the nuclear spins for the axion dark matter detection. Our method has the potential to be sensitive to a broad frequency range <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo>≲</mo><mn>100</mn><mtext> </mtext><mtext> </mtext><mrow><mi>Hz</mi></mrow></mrow></math> corresponding to the axion mass <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>m</mi></mrow><mrow><mi>a</mi></mrow></msub><mo>≲</mo><mn>4</mn><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>13</mn></mrow></msup><mtext> </mtext><mtext> </mtext><mi>eV</mi></mrow></math>. We present the detection limit of our method for both the axion-neutron and the axion-proton couplings and discuss its significance in comparison with other proposed ideas. We also show that the sensitivities of the NV center sensor to various spin species will open up new directions for constructing protocols that can mitigate magnetic noise effects.

Japan

So Chigusa

Taiwan

Masashi Hazumi

Ernst David Herbschleb

Yuichiro Matsuzaki

Norikazu Mizuochi

Kazunori Nakayama

Nuclear spin metrology with nitrogen vacancy center in diamond for axion dark matter detection

We construct the phase space of a spherically symmetric causal diamond in (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>d</mi><mo>+</mo><mn>2</mn></mrow></math>)-dimensional Minkowski spacetime. Utilizing the covariant phase space formalism, we identify the relevant degrees of freedom that localize to the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>d</mi></math>-dimensional bifurcate horizon and, upon canonical quantization, determine their commutators. On this phase space, we find two Iyer-Wald charges. The first of these charges, proportional to the area of the causal diamond, is responsible for shifting the null time along the horizon and has been well documented in the literature. The second charge is much less understood, being integrable for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>d</mi><mo>≥</mo><mn>2</mn></math> only if we allow for field-dependent diffeomorphisms and is responsible for changing the size of the causal diamond.

Mathew W. Bub

Netherlands

Prahar Mitra

Yiwen Zhang

Kathryn M. Zurek

Quantum Mechanics of a Spherically Symmetric Causal Diamond in Minkowski Spacetime

A numerical setup for the Bell-CHSH inequality for causal diamonds in $$1+1$$ Minkowski spacetime is presented. Upon choosing a suitable set of test functions supported in the diamonds, sensible violations are reported for the correlation function of Weyl operators of a real scalar massive field in the vacuum state.

Brazil

M. Guimaraes

Switzerland

I. Roditi

S. Sorella

Investigation of the Bell-CHSH inequality in diamond regions

Recent work has shown that certain integrable and conformal field theories in two dimensions can be given a higher-dimensional origin from holomorphic Chern-Simons in six dimensions. Along with anti-self-dual Yang-Mills and four-dimensional Chern-Simons, this gives rise to a diamond correspondence of theories. In this work we extend this framework to incorporate models realised through gaugings. As well as describing a higher-dimensional origin of coset CFTs, by choosing the details of the reduction from higher dimensions, we obtain rich classes of two-dimensional integrable models including homogeneous sine-Gordon models and generalisations that are new to the literature.

United Kingdom

Lewis Cole

Ryan Cullinan

Ben Hoare

Argentina

Joaquin Liniado

Belgium

Daniel Thompson

Gauging the diamond: integrable coset models from twistor space

We demonstrate a tree-level equivalence between four distinct infrared objects in (<math><mrow><mi>d</mi><mo>+</mo><mn>2</mn></mrow></math>)-dimensional Abelian gauge theories. These are (i) the large gauge charge <math><msub><mi>Q</mi><mi>ϵ</mi></msub></math> where the function <math><mi>ϵ</mi></math> on the sphere parametrizing large gauge transformations is identified with the Goldstone mode <math><mi>θ</mi></math> of spontaneously broken large gauge symmetry; (ii) the soft effective action that captures the dynamics of the soft and Goldstone modes; (iii) the edge mode action with Neumann boundary conditions; and (iv) the Wilson line dressing of a scattering amplitude, including a novel dressing for soft photons, which have local charge distributions despite having vanishing global charge. The promotion of the large gauge parameter to the dynamical Goldstone and the novel dressing of soft gauge particles give rise to intriguing possibilities for the future study of infrared dynamics of gauge theories and gravity.

Diamond of infrared equivalences in abelian gauge theories

We demonstrate a novel mechanism for producing dark compact objects and black holes through a dark sector, where all the dark matter can be dissipative. Heavy dark sector particles with masses above <math><msup><mn>10</mn><mn>4</mn></msup><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math> can come to dominate the Universe and yield an early matter-dominated era before big bang nucleosynthesis (BBN). Density perturbations in this epoch can grow and collapse into tiny dark matter halos, which cool via self-interactions. The typical halo size is set by the Hubble length once perturbations begin growing, offering a straightforward prediction of the halo size and evolution depending on one’s choice of dark matter model. Once these primordial halos have formed, a thermal phase transition can then shift the Universe back into radiation domination and standard cosmology. These halos can continue to collapse after BBN, resulting in the late-time formation of fragmented dark compact objects and sub-solar-mass primordial black holes. We find that these compact objects can constitute a sizable fraction of all of dark matter. The resulting fragments can have masses between <math><msup><mn>10</mn><mn>20</mn></msup></math> and <math><msup><mn>10</mn><mn>32</mn></msup><mtext> </mtext><mtext> </mtext><mi>g</mi></math>, with radii ranging from <math><msup><mn>10</mn><mrow><mo>−</mo><mn>2</mn></mrow></msup></math> to <math><msup><mn>10</mn><mn>5</mn></msup><mtext> </mtext><mtext> </mtext><mi>m</mi></math>, while the black holes can have masses between <math><msup><mn>10</mn><mn>8</mn></msup></math> and <math><msup><mn>10</mn><mn>34</mn></msup><mtext> </mtext><mtext> </mtext><mi>g</mi></math>. Furthermore, a unique feature of this model is the late-time formation of black holes which can evaporate today. We compare where these objects lie with respect to current primordial black hole and massive (astrophysical) compact halo object constraints.

Canada

Joseph Bramante

Christopher V. Cappiello

Melissa Diamond

J. Leo Kim

Qinrui Liu

Aaron C. Vincent

Dissipative dark cosmology: From early matter dominance to delayed compact objects