arXiv subjects

Kari Rummukainen

Publications and source records attributed to Kari Rummukainen.

At least 37 records · Page 2Linked to original sources

arXiv2022

Holographic spacetime from lattice Yang-Mills theory

Entanglement entropy is a notoriously difficult quantity to compute in strongly interacting gauge theories. Existing lattice replica methods have suffered from a severe signal-to-noise ratio problem, making high-precision studies prohibitively expensive. Our improved lattice method mitigates this situation and allows us to probe holographic predictions for the behavior of entanglement entropies in three- and four-dimensional Yang-Mills theories. We use this data for the numerical reconstruction of holographic bulk metrics.

hep-th↗

arXiv2022

Improved lattice method for determining entanglement measures in SU(N) gauge theories

The determination of entanglement measures in SU(N) gauge theories is a non-trivial task. With the so-called "replica trick", a family of entanglement measures, known as "Rényi entropies", can be determined with lattice Monte Carlo. Unfortunately, the standard implementation of the replica method for SU(N) lattice gauge theories suffers from a severe signal-to-noise ratio problem, rendering high-precision studies of Rényi entropies prohibitively expensive. In this work, we propose a method to overcome the signal-to-noise ratio problem and show some first results for SU(N) in 4 dimensions.

hep-lat↗

arXiv2022

Decay of acoustic turbulence in two dimensions and implications for cosmological gravitational waves

Gravitational waves from a phase transition associated with the generation of the masses of elementary particles are within the reach of future space-based detectors such as LISA. A key determinant of the resulting power spectrum, not previously studied, is the lifetime of the acoustic turbulence which follows. We study decaying acoustic turbulence using numerical simulations of a relativistic fluid in two dimensions. Working in the limit of non-relativistic bulk velocities, with an ultra-relativistic equation of state, we find that the energy spectrum evolves towards a self-similar broken power law, with a high-wavenumber behaviour of $k^{-2.08 \pm 0.08}$, cut off at very high $k$ by the inverse width of the shock waves. Our model for the decay of acoustic turbulence can be extended to three dimensions using the universality of the high-$k$ power law and the evolution laws for the kinetic energy and the integral length scale. It is used to build an estimate for the gravitational wave power spectrum resulting from a collection of shock waves, as might be found in the aftermath of a strong first order phase transition in the early universe. The power spectrum has a peak wavenumber set by the initial length scale of the acoustic waves, and a new secondary scale at a lower wavenumber set by the integral scale after a Hubble time. Between these scales a distinctive new power law appears. Our results allow more accurate predictions of the gravitational wave power spectrum for a wide range of early universe phase transition scenarios.

gr-qc↗

arXiv2022

Generation of gravitational waves from freely decaying turbulence

We study the stochastic gravitational wave background (SGWB) produced by freely decaying vortical turbulence in the early Universe. We thoroughly investigate the time correlation of the velocity field, and hence of the anisotropic stresses producing the gravitational waves. With hydrodynamical simulations, we show that the unequal time correlation function (UETC) of the Fourier components of the velocity field is Gaussian in the time difference, as predicted by the "sweeping" decorrelation model. We introduce a decorrelation model that can be extended to wavelengths around the integral scale of the flow. Supplemented with the evolution laws of the kinetic energy and of the integral scale, this provides a new model UETC of the turbulent velocity field consistent with the simulations. We discuss the UETC as a positive definite kernel, and propose to use the Gibbs kernel for the velocity UETC as a natural way to ensure positive definiteness of the SGWB. The SGWB is given by a 4-dimensional integration of the resulting anisotropic stress UETC with the gravitational wave Green's function. We perform this integration using a Monte Carlo algorithm based on importance sampling, and find that the result matches that of the simulations. Furthermore, the SGWB obtained from the numerical integration and from the simulations show close agreement with a model in which the source is constant in time and abruptly turns off after a few eddy turnover times. Based on this assumption, we provide an approximate analytical form for the SGWB spectrum and its scaling with the initial kinetic energy and integral scale. Finally, we use our model and numerical integration algorithm to show that including an initial growth phase for the turbulent flow heavily influences the spectral shape of the SGWB. This highlights the importance of a complete understanding of the turbulence generation mechanism.

astro-ph.CO↗

arXiv2022

Non-perturbative decoupling of massive fermions

SU(2) gauge theory with Nf=24 massless fermions is non-interacting at long distances, i.e. it has an infrared fixed point at vanishing coupling. With massive fermions the fermions are expected to decouple at energy scales below the fermion mass, and the infrared behaviour is that of confining SU(2) pure gauge theory. We demonstrate this behaviour non-perturbatively with lattice Monte Carlo simulations by measuring the gradient flow running coupling.

hep-lat↗

arXiv2022

Infrared physics of the 3D SU(2) adjoint Higgs model at the crossover transition

We study the crossover phase transition of the SU(2) Georgi-Glashow model in three dimensions. In this model, a confining condensate of topological 't Hooft-Polyakov monopoles exists in the Higgs regime. We use lattice Monte Carlo simulations to study the monopole gas across a crossover transition, and demonstrate that gradient flow can be used to renormalize the otherwise divergent monopole number density. The condensation of the monopoles means that the theory admits also a massive photon-like excitation. We show that the renormalized monopole number density is approximately proportional to the square of the photon mass, in agreement with semiclassical results. Our results give insight into behaviour of the Higgs regime near crossover, which has boarder implications for beyond the Standard Model theories containing adjoint scalar fields.

hep-lat↗

arXiv2021

Infrared physics of the $\mathrm{SU}(2)$ Georgi-Glashow crossover transition

We perform a lattice study of the phase transition in the $\mathrm{SU}(2)$ Georgi-Glashow model in three dimensions, where the gauge symmetry is broken to $\mathrm{U}(1)$ by the Higgs mechanism and a photon-like state appears. Due to condensation of monopoles the photon acquires a mass, which depends on the number density of the monopoles. We show that the monopole density can be renormalised on the lattice using gradient flow. Our preliminary results suggest that Polyakov's semiclassical relation between the photon mass and the renormalised monopole density is valid also at the nonperturbative level.

hep-lat↗

arXiv2021

SU(2) gauge theory with $N_f=24$ quarks at non-zero mass

We study SU(2) gauge field theory with $N_f=24$ quarks. The theory is asymptotically non-free and, at vanishing quark mass, governed by a Gaussian fixed point at long distances. On the other hand, at non-zero quark mass the quarks are expected to decouple at long distances and the system behaves like confining pure gauge SU(2) theory. We study the mass spectrum of the theory as the quark mass is varied and obtain scaling laws for meson masses and string tension. We also measure the evolution of the coupling constant at non-zero quark mass with gradient flow method. We observe unambiguously the decoupling of the quarks with the associated change of evolution of the coupling constant.

hep-lat↗

arXiv2021

Bulk-preventing actions for SU(N) gauge theories

We introduce a one-parameter family of SU(N) gauge actions which, when used in combination with an HMC update algorithm, prevent the gauge system from entering an artificial bulk-"phase". We briefly discuss the mechanism behind the bulk-prevention and present test results for different SU(N) gauge groups.

hep-lat↗

arXiv2021

High order quark number susceptibilities in hot QCD from lattice EQCD

Building on the experience of [1], we develop a formalism to construct operators for higher derivatives of the pressure in hot QCD with respect to the quark chemical potential $μ$. We provide formulae for the operators up to the sixth derivative, and obtain continuum-extrapolated results from lattice EQCD at zero and finite $μ$ and at six different pairs of temperature T and number of massless quark flavors $n_f$. Our data is benchmarked against full-QCD lattice and perturbative results, allowing to judge the quality of the perturbative series expansion in EQCD and the dimensional reduction procedure as a whole.

hep-lat↗

arXiv2021

Spectrum of SU(2) gauge theory at large number of flavors

We present a numerical study of the spectrum of an asymptotically non-free $SU(2)$ gauge theory with $N_f=24$ massive fermion flavors. For such large number of flavors, asymptotic freedom is lost and the massless theory is governed by a gaussian fixed point at long distances. If fermions are massive they decouple at low energy scales and the theory is confining. We present a scaling law for the masses of the hadrons, glueballs and string tension as functions of fermion mass. The hadrons become effectively heavy quark systems, with masses approximately twice the fermion mass, whereas the energy scale of the confinement, probed by e.g. the string tension, is much smaller and vanishes asymptotically as $m_\text{fermion}^{2.18}$. Our results from lattice simulations are compatible with this behaviour.

hep-lat↗

arXiv2021

Detecting gravitational waves from cosmological phase transitions with LISA: an update

We investigate the potential for observing gravitational waves from cosmological phase transitions with LISA in light of recent theoretical and experimental developments. Our analysis is based on current state-of-the-art simulations of sound waves in the cosmic fluid after the phase transition completes. We discuss the various sources of gravitational radiation, the underlying parameters describing the phase transition and a variety of viable particle physics models in this context, clarifying common misconceptions that appear in the literature and identifying open questions requiring future study. We also present a web-based tool, PTPlot, that allows users to obtain up-to-date detection prospects for a given set of phase transition parameters at LISA.

astro-ph.CO↗

arXiv2020

Shape of the acoustic gravitational wave power spectrum from a first order phase transition

We present results from large-scale numerical simulations of a first order thermal phase transition in the early universe, in order to explore the shape of the acoustic gravitational wave and the velocity power spectra. We compare the results with the predictions of the recently proposed sound shell model. For the gravitational wave power spectrum, we find that the predicted $k^{-3}$ behaviour, where $k$ is the wavenumber, emerges clearly for detonations. The power spectra from deflagrations show similar features, but exhibit a steeper high-$k$ decay and an extra feature not accounted for in the model. There are two independent length scales: the mean bubble separation and the thickness of the sound shell around the expanding bubble of the low temperature phase. It is the sound shell thickness which sets the position of the peak of the power spectrum. The low wavenumber behaviour of the velocity power spectrum is consistent with a causal $k^{3}$, except for the thinnest sound shell, where it is steeper. We present parameters for a simple broken power law fit to the gravitational wave power spectrum for wall speeds well away from the speed of sound where this form can be usefully applied. We examine the prospects for the detection, showing that a LISA-like mission has the sensitivity to detect a gravitational wave signal from sound waves with an RMS fluid velocity of about $0.05c$, produced from bubbles with a mean separation of about $10^{-2}$ of the Hubble radius. The shape of the gravitational wave power spectrum depends on the bubble wall speed, and it may be possible to estimate the wall speed, and constrain other phase transition parameters, with an accurate measurement of a stochastic gravitational wave background.

astro-ph.CO↗

arXiv2019

Safety versus triviality on the lattice

We present the first numerical study of the ultraviolet dynamics of non-asymptotically free gauge-fermion theories at large number of matter fields. As testbed theories we consider non-abelian SU(2) gauge theories with 24 and 48 Dirac fermions on the lattice. For these number of flavors asymptotic freedom is lost and the theories are governed by a gaussian fixed point at low energies. In the ultraviolet they can develop a physical cutoff and therefore be trivial, or achieve an interacting safe fixed point and therefore be fundamental at all energy scales. We demonstrate that the gradient flow method can be successfully implemented and applied to determine the renormalized running coupling when asymptotic freedom is lost. Additionally, we prove that our analysis is connected to the gaussian fixed point as our results nicely match with the perturbative beta function. Intriguingly, we observe that it is hard to achieve large values of the renormalized coupling on the lattice. This might be an early sign of the existence of a physical cutoff and imply that a larger number of flavors is needed to achieve the safe fixed point. A more conservative interpretation of the results is that the current lattice action is unable to explore the deep ultraviolet region where safety might emerge. Our work constitutes an essential step towards determining the ultraviolet fate of non asymptotically free gauge theories.

hep-lat↗

arXiv2019

On the validity of perturbative studies of the electroweak phase transition in the Two Higgs Doublet model

Making use of a dimensionally-reduced effective theory at high temperature, we perform a nonperturbative study of the electroweak phase transition in the Two Higgs Doublet model. We focus on two phenomenologically allowed points in the parameter space, carrying out dynamical lattice simulations to determine the equilibrium properties of the transition. We discuss the shortcomings of conventional perturbative approaches based on the resummed effective potential - regarding the insufficient handling of infrared resummation but also the need to account for corrections beyond 1-loop order in the presence of large scalar couplings - and demonstrate that greater accuracy can be achieved with perturbative methods within the effective theory. We find that in the presence of very large scalar couplings, strong phase transitions cannot be reliably studied with any of the methods.

hep-ph↗

arXiv2018

Infrared Behaviour of SU(2) Gauge Theory with $N_f$ fundamental flavours

We review our recent results on the infrared behaviour of the SU(2) gauge theory with $N_f$ massless fundamental flavour fermions. We have analyzed the running of the coupling in SU(2) gauge theories with six and eight fermionic flavours using the gradient flow step scaling method. From the running of the coupling, we see a clear indication of an infrared stable fixed point in theories with six and eight flavours. These results are confirmed by our mass spectrum study, where we varied the number of flavours from two to six. We also compute the anomalous dimensions of mass and coupling.

hep-lat↗

arXiv2018

Infrared fixed point of SU(2) gauge theory with six flavors

We compute the running of the coupling in SU(2) gauge theory with six fermions in fundamental representation of the gauge group. We establish an infrared stable fixed point at strong coupling and measure also the anomalous dimension of the fermion mass operator at the fixed point. This theory therefore likely lies close to the boundary of the conformal window and will display novel infrared dynamics if coupled with the electroweak sector of the Standard Model.

hep-lat↗

arXiv2018

Slope of the beta function at the fixed point of SU(2) gauge theory with six or eight flavors

We consider measurement of the leading irrelevant scaling exponent $γ_g^\ast$, given by the slope of the beta function, at the fixed point of SU(2) gauge theory with six or eight flavors. We use the running coupling measured using the gradient flow method and perform the continuum extrapolation by interpolating the measured beta function. We study also the dependence of the results on different discretization of the flow. For the eight flavor theory we find $γ_g^\ast=0.19(8)_{-0.09}^{+0.21}$. Applying the same analysis also for the six flavor theory, we find $γ_g^\ast=0.648(97)_{-0.1}^{+0.16}$ consistently with the earlier analysis.

hep-lat↗