We study the formation of primordial black holes (PBHs) and stochastic gravitational waves background (SGWB) produced by the supercooled radion phase transition (PT) in warped extra-dimension models solving the gauge hierarchy problem. We first determine how the SGWB and the produced PBH mass and abundance depend on the warped model’s infrared energy scale $\textit{ρ}$, and the number of holographic colors $\textit{N}$. With this finding, we recast on the plane {$\textit{ρ}$, $\textit{N}$} the current SGWB and PBH constraints, as well as the expected parameter reaches of GW detectors, as LISA and ET, and the gravitational lensing ones, such as NGRST. On the same plane, we also map the collider bounds on massive graviton production, and cosmological bounds on the radion phenomenology. We find that, for $\textit{N}$ ∼ 10 − 50, the considered PT predicts a PBH population mass in the range $\textit{M}$ ∼ (10 − 10 )$\textit{M}$ for $\textit{ρ}$ ∼ (10 − 10 ) TeV. In the range $\textit{ρ}$ ≃ (0.05 − 0.5) GeV, it can explain the recent SGWB hint at nHz frequencies and generate PBH binaries with mass $\textit{M}$ ∼ (0.1 – 1)$\textit{M}$ detectable at LISA and ET. The experimentally allowed mass region where PBHs can account for the whole dark matter abundance, and are produced with a tuning ≲ 10 , corresponds to 10 TeV ≲ $\textit{ρ}$ ≲ 10 TeV. These PBHs can compensate the lack of natural candidates for dark matter in warped extra dimensional models. Such a region represents a great science case where forthcoming and future colliders like HE-LHC and FCC-hh, gravitational-wave observatories and other PBHs probes play a key complementary role.

Poland

Anish Ghoshal

Spain

Eugenio Megías

Norway

Germano Nardini

Mariano Quirós

Complementary probes of warped extra dimension: colliders, gravitational waves and primordial black holes from phase transitions

We study holographic entanglement entropy and revisit thermodynamics and confinement in the dilaton-gravity system. Our analysis focuses on a solvable class of backgrounds that includes AdS and linear dilaton spacetimes as particular cases, with some results extended to general warped metrics. A general lesson is that the behavior of the holographic theory is tied to the bulk curvature singularities. We find that a singular background is confining if and only if $\textit{i)}$ the singularity coincides with a boundary or $\textit{ii)}$ it is the linear dilaton. In the former case, for which the singularity cuts off spacetime, we demonstrate that both entanglement entropy and thermodynamics exhibit a first order phase transition. In the linear dilaton case we find instead that both entanglement entropy and thermal phase transitions are of second order. Additionally, along the process we thoroughly derive the radion effective action at quadratic order.

Brazil

Sergio Barbosa

Sylvain Fichet

Entanglement entropy and thermal phase transitions from curvature singularities

We propose a setup for the origin of dark matter based on spacetime with a warped extra dimension and three branes: the Planck brane, the TeV brane, at a (few) TeV scale <math><mrow><msub><mrow><mi>ρ</mi></mrow><mrow><mi>T</mi></mrow></msub></mrow></math>, and a dark brane, at a (sub-)GeV scale <math><msub><mi>ρ</mi><mn>1</mn></msub><mo>≲</mo><mn>100</mn><mtext> </mtext><mtext> </mtext><mrow><mi>GeV</mi></mrow><mo>≪</mo><msub><mi>ρ</mi><mi>T</mi></msub></math>. The Standard Model (SM) is localized in the TeV brane, thus solving the Higgs hierarchy problem, while the dark matter <math><mi>χ</mi></math>, a Dirac fermion with mass <math><msub><mi>m</mi><mi>χ</mi></msub><mo>&lt;</mo><msub><mi>ρ</mi><mn>1</mn></msub></math>, is localized in the dark brane. The radion, with mass <math><msub><mi>m</mi><mi>r</mi></msub><mo>&lt;</mo><msub><mi>m</mi><mi>χ</mi></msub></math>, interacts strongly [<math><mrow><mo>∼</mo><msub><mrow><mi>m</mi></mrow><mrow><mi>χ</mi></mrow></msub><mo>/</mo><msub><mrow><mi>ρ</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>∼</mo><mi>O</mi><mo>(</mo><mn>1</mn><mo>)</mo></mrow></math>] with dark matter and very weakly (<math><mo>∼</mo><msub><mi>m</mi><mi>f</mi></msub><msub><mi>ρ</mi><mn>1</mn></msub><mo>/</mo><msubsup><mi>ρ</mi><mi>T</mi><mn>2</mn></msubsup><mo>≪</mo><mn>1</mn></math>) with the Standard Model matter <math><mi>f</mi></math>. The generic conflict between the bounds on its detection signatures and its proper relic abundance is avoided as dark matter annihilation is <math><mi>p</mi></math>-wave suppressed. The former is determined by its very weak interactions with the SM and the latter by its much stronger annihilation into radions. Therefore, there is a vast range in the dark matter’s parameter space where the correct relic abundance is achieved consistently with the existing bounds. Moreover, for the dark brane with <math><msub><mi>ρ</mi><mn>1</mn></msub><mo>≲</mo><mn>3</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>, a confinement/deconfinement first order phase transition, where the radion condensates, produces a stochastic gravitational wave background at the nanohertz frequencies, which can be identified with the signal detected by the Pulsar Timing Array (PTA) experiments. In the PTA window, for <math><mn>0.15</mn><mo>≲</mo><msub><mi>m</mi><mi>χ</mi></msub><mo>≲</mo><mn>2</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math> the relic abundance is reproduced and all constraints are satisfied.

Fotis Koutroulis

Stefan Pokorski

Dark branes for dark matter

We study a solvable class of five-dimensional dilaton gravity models that continuously interpolate between anti-de Sitter (AdS5), linear dilaton (LD5) and positively curved spacetimes as a function of a continuous parameter ν. The dilaton vacuum expectation value is set by a potential localized on a flat brane. We chart the elementary properties of these backgrounds for any admissible ν, and determine stability conditions of the brane-dilaton system. We find that the spectrum of metric fluctuations can be either continuous or discrete. It features a massless graviton mode confined between the brane and the curvature singularity, and a massive radion mode tied to brane-dilaton stability. We show that, in the presence of a bulk black hole, the holographic theory living on the brane features a perfect fluid. The equation of state of the holographic fluid interpolates between radiation, pressureless matter and vacuum energy as a function of ν. This extends earlier findings on holographic fluids. Our results suggest that the thermodynamics of the fluid mirrors precisely the thermodynamics of the bulk black hole.

Holographic fluids from 5D dilaton gravity

Using the Plastino-Plastino (PP) equation, we calculate transport coefficients of the heavy-quarks traversing inside the quark-gluon plasma, and generalize their relationship with differential energy loss. The PP equation indicates anomalous diffusion of the probe particles and yields a quasi-exponential stationary distribution obtained also from the nonadditive statistics proposed by C. Tsallis. We estimate energy loss in a nonadditive quark-gluon medium, and calculate the jet quenching parameter (<math><mover><mrow><mi>q</mi></mrow><mrow><mo>ˆ</mo></mrow></mover></math>) for the PP dynamics. With the help of the estimate of <math><mover><mrow><mi>q</mi></mrow><mrow><mo>ˆ</mo></mrow></mover></math>, we calculate the nuclear suppression factor (<math><msub><mrow><mi>R</mi></mrow><mrow><mtext>AA</mtext></mrow></msub></math>) of the heavy-quarks passing through a nonadditive quark-gluon plasma using the model proposed by Dokshitzer and Kharzeev. In many a case, the parameters in the analysis are fixed from the experimental results to minimize arbitrariness. There is a good agreement between the theoretical calculation and experimental <math><msub><mrow><mi>R</mi></mrow><mrow><mtext>AA</mtext></mrow></msub></math> data, indicating that fast heavy-quarks may be subjected to anomalous diffusion inside the QGP.

JINR

Trambak Bhattacharyya

Airton Deppman

Jet quenching of the heavy quarks in the quark-gluon plasma and the nonadditive statistics

Particle production yields measured in central Au-Au collision at RHIC are obtained with free Fermi and Bose gases and also with a replacement of these statistics by non-extensive statistics. For the latter calculation, a set of different parameters was used with values of the Tsallis parameter q chosen between 1.01 and 1.25, with 1.16 generating the best agreement with experimental data, an indication that non-extensive statistics may be one of the underlying features in heavy ion-collisions.

Juliana O. Costa

Isabelle Aguiar

Jadna L. Barauna

Tiago N. da Silva

Débora P. Menezes

Non-extensive statistics in Au-Au collisions

Unstable particles decay sooner or later, so they are not described by asymptotic one-particle states and they should not be included as independent states in unitarity relations such as the optical theorem. The same applies to any countable collection of unstable particles. We show that the behaviour of unparticle stuff, that is, a continuous collection of particles with different masses and common decay channels, is pretty different: it has a non-vanishing probability of surviving for ever and the corresponding asymptotic states must be taken into account to comply with unitarity. We also discuss compressed spectra and the transition from the discrete to the continuous case.

Manuel Pérez-Victoria

Undecay

The linear dilaton (LD) background is the keystone of a string-derived holographic correspondence beyond <math><mrow><msub><mrow><mi>AdS</mi></mrow><mrow><mi>d</mi><mo>+</mo><mn>1</mn></mrow></msub><mo>/</mo><msub><mrow><mi>CFT</mi></mrow><mrow><mi>d</mi></mrow></msub></mrow></math>. This motivates an exploration of the (<math><mrow><mi>d</mi><mo>+</mo><mn>1</mn></mrow></math>)-dimensional linear dilaton spacetime (<math><mrow><msub><mrow><mi>LD</mi></mrow><mrow><mi>d</mi><mo>+</mo><mn>1</mn></mrow></msub></mrow></math>) and its holographic properties from the low-energy viewpoint. We first notice that the <math><mrow><msub><mrow><mi>LD</mi></mrow><mrow><mi>d</mi><mo>+</mo><mn>1</mn></mrow></msub></mrow></math> space has simple conformal symmetries, that we use to shape an effective field theory (EFT) on the LD background. We then place a brane in the background to study holography at the level of quantum fields and gravity. We find that the holographic correlators from the EFT feature a pattern of singularities at certain kinematic thresholds. We argue that such singularities can be used to bootstrap the putative <math><mi>d</mi></math>-dimensional dual theory using techniques analogous to those of the cosmological bootstrap program. Turning on finite temperature, we study the holographic fluid emerging on the brane in the presence of a bulk black hole. We find that the holographic fluid is pressureless for any <math><mi>d</mi></math> due to a cancellation between Weyl curvature and dilaton stress tensor, and verify consistency with the time evolution of the theory. From the fluid thermodynamics, we find a universal temperature and Hagedorn behavior for any <math><mi>d</mi></math>. This matches the properties of a <math><mrow><msub><mrow><mi>CFT</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></math> with large <math><mi>T</mi><mover><mi>T</mi><mo>¯</mo></mover></math> deformation, and of little string theory for <math><mi>d</mi><mo>=</mo><mn>6</mn></math>. We also find that the holographic fluid entropy exactly matches the bulk black hole Bekenstein-Hawking entropy. Both the fluid equation of state and the spectrum of quantum fluctuations suggest that the <math><mi>d</mi></math>-dimensional dual theory arising from <math><mrow><msub><mrow><mi>LD</mi></mrow><mrow><mi>d</mi><mo>+</mo><mn>1</mn></mrow></msub></mrow></math> is generically gapped.

Holography of linear dilaton spacetimes from the bottom up

Nondissipative transport of strangeness is studied in a chiral hadronic plasma with three flavors. In the phase in which chiral symmetry is preserved, strangeness transport is found to be driven by both an external magnetic field and fluid vorticity. As for the constitutive relations of the baryon and electromagnetic currents, they exhibit vortical terms proportional to the strangeness chemical potential. In the superfluid phase, transverse nondissipative diffusion of the baryon, electromagnetic, and strangeness charges is found, which survives in the limit of vanishing chiral imbalance and mixes in a fashion similar to standard dissipative diffusion in quark-gluon plasma.

Miguel Vázquez-Mozo

Anomalous strangeness transport

This study investigates the interconnections between the traditional Fokker-Planck Equation (FPE) and its fractal counterpart (FFPE), utilizing fractal derivatives. By examining the continuous approximation of fractal derivatives in the FPE, it derives the Plastino-Plastino Equation (PPE), which is commonly associated with Tsallis Statistics. This work deduces the connections between the entropic index and the geometric quantities related to the fractal dimension. Furthermore, it analyzes the implications of these relationships on the dynamics of systems in fractal spaces. To assess the effectiveness of both equations, numerical solutions are compared within the context of complex systems dynamics, specifically examining the behaviours of quark-gluon plasma (QGP). The FFPE provides an appropriate description of the dynamics of fractal systems by accounting for the fractal nature of the momentum space, exhibiting distinct behaviours compared to the traditional FPE due to the system's fractal nature. The findings indicate that the fractal equation and its continuous approximation yield similar results in studying dynamics, thereby allowing for interchangeability based on the specific problem at hand.