arXiv subjects

K. Kajantie

Publications and source records attributed to K. Kajantie.

At least 37 records · Page 2Linked to original sources

arXiv2009

Isotropic AdS/CFT fireball

We study the AdS/CFT thermodynamics of the spatially isotropic counterpart of the Bjorken similarity flow in d-dimensional Minkowski space with d>=3, and of its generalisation to linearly expanding d-dimensional Friedmann-Robertson-Walker cosmologies with arbitrary values of the spatial curvature parameter k. The bulk solution is a nonstatic foliation of the generalised Schwarzschild-AdS black hole with a horizon of constant curvature k. The boundary matter is an expanding perfect fluid that satisfies the first law of thermodynamics for all values of the temperature and the spatial curvature, but it admits a description as a scale-invariant fluid in local thermal equilibrium only when the inverse Hawking temperature is negligible compared with the spatial curvature length scale. A Casimir-type term in the holographic energy-momentum tensor is identified from the threshold of black hole formation and is shown to take different forms for k>=0 and k<0.

hep-th↗

arXiv2009

Casimir energy in the gauge/gravity description of Bjorken flow?

In the AdS/CFT description of four-dimensional QCD matter undergoing Bjorken expansion, does the holographic energy-momentum tensor contain a Casimir-type contribution that should not be attributed to thermal matter? When the bulk isometry ansatz that yielded such a Casimir term for (1+1)-dimensional boundary matter is generalised to a four-dimensional boundary, we show that a Casimir term does not arise, owing to singularities in the five-dimensional bulk solution. The geometric reasons are traced to a difference between the isometries of AdS_3 and AdS_{d+1} for d>=3.

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arXiv2008

Three-dimensional physics and the pressure of hot QCD

We update Monte Carlo simulations of the three-dimensional SU(3) + adjoint Higgs theory, by extrapolating carefully to the infinite volume and continuum limits, in order to estimate the contribution of the infrared modes to the pressure of hot QCD. The sum of infrared contributions beyond the known 4-loop order turns out to be a smooth function, of a reasonable magnitude and specific sign. Unfortunately, adding this function to the known 4-loop terms does not improve the match to four-dimensional lattice data, in spite of the fact that other quantities, such as correlation lengths, spatial string tension, or quark number susceptibilities, work well within the same setup. We outline possible ways to reduce the mismatch.

hep-lat↗

arXiv2008

Gravity dual of conformal matter collisions in 1+1 dimensions

We find the three-dimensional gravity dual of a process in which two clouds of (1+1)-dimensional conformal matter moving in opposite directions collide. This gives the most general conformally invariant holographic flow in the 1+1 dimensional boundary theory in terms of two arbitrary functions. With a suitable choice of the arbitrary functions the process can be interpreted as an opaque collision of two extended systems with central, fragmentation and interaction regions. Comparison with classical gluon field calculations relates the size of the system with the saturation scale.

hep-th↗

arXiv2007

Gravity dual of 1+1 dimensional Bjorken expansion

We study the application of AdS/CFT duality to longitudinal boost invariant Bjorken expansion of QCD matter produced in ultrarelativistic heavy ion collisions. As the exact (1+4)-dimensional bulk solutions for the (1+3)-dimensional boundary theory are not known, we investigate in detail the (1+1)-dimensional boundary theory, where the bulk is AdS_3 gravity. We find an exact bulk solution, show that this solution describes part of the spinless Banados-Teitelboim-Zanelli (BTZ) black hole with the angular dimension unwrapped, and use the thermodynamics of the BTZ hole to recover the time-dependent temperature and entropy density on the boundary. After separating from the holographic energy-momentum tensor a vacuum contribution, given by the extremal black hole limit in the bulk, we find that the boundary fluid is an ideal gas in local thermal equilibrium. Including angular momentum in the bulk gives a boundary flow that is boost invariant but has a nonzero longitudinal velocity with respect to the Bjorken expansion.

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arXiv2007

Spherically expanding matter in AdS/CFT

We discuss an exact time dependent O(3) symmetric solution with a horizon of the 5d AdS classical gravity equations searching for a 4d boundary theory which would correspond to expanding gauge theory matter. The boundary energy-momentum tensor and entropy density are computed. The boundary metric is the flat Friedmann one and any time dependence on the boundary is incompatible with Minkowski metric. However, at large times when curvature effects are negligible, perfect fluid behavior arises in a natural way.

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arXiv2006

Thermodynamics of AdS/QCD

We study finite temperature properties of four dimensional QCD-like gauge theories in the gauge theory/gravity duality picture. The gravity dual contains two deformed 5d AdS metrics, with and without a black hole, and a dilaton. We study the thermodynamics of the 4d boundary theory and constrain the two metrics so that they correspond to a high and a low temperature phase separated by a first order phase transition. The equation of state has the standard form for the pressure of a strongly coupled fluid modified by a vacuum energy, a bag constant. We determine the parameters of the deformation by using QCD results for $T_c$ and the hadron spectrum. With these parameters, we show that the phase transition in the 4d boundary theory and the 5d bulk Hawking-Page transition agree. We probe the dynamics of the two phases by computing the quark-antiquark free energy in them and confirm that the transition corresponds to confinement-deconfinement transition.

hep-ph↗

arXiv2006

The pressure of deconfined QCD for all temperatures and quark chemical potentials

We present a new method for the evaluation of the perturbative expansion of the QCD pressure which is valid at all values of the temperature and quark chemical potentials in the deconfined phase and which we work out up to and including order g^4 accuracy. Our calculation is manifestly four-dimensional and purely diagrammatic -- and thus independent of any effective theory descriptions of high temperature or high density QCD. In various limits, we recover the known results of dimensional reduction and the HDL and HTL resummation schemes, as well as the equation of state of zero-temperature quark matter, thereby verifying their respective validity. To demonstrate the overlap of the various regimes, we furthermore show how the predictions of dimensional reduction and HDL resummed perturbation theory agree in the regime T~\sqrt{g}*mu. At parametrically smaller temperatures T~g*mu, we find that the dimensional reduction result agrees well with those of the nonstatic resummations down to the remarkably low value T~0.2 m_D, where m_D is the Debye mass at T=0. Beyond this, we see that only the latter methods connect smoothly to the T=0 result of Freedman and McLerran, to which the leading small-T corrections are given by the so-called non-Fermi-liquid terms, first obtained through HDL resummations. Finally, we outline the extension of our method to the next order, where it would include terms for the low-temperature entropy and specific heats that are unknown at present.

hep-ph↗

arXiv2006

Chemical thermalization in relativistic heavy ion collisions

We compute by numerical integration of the Dirac equation the number of quark-antiquark pairs initially produced in the classical color fields of colliding ultrarelativistic nuclei. While the number of qqbar pairs is parametrically suppressed in the coupling constant, we find that in this classical field model their production rate is comparable to the thermal ratio of gluons/pairs = 9 N_f/32. After isotropization one thus would have quark-gluon plasma in chemical equilibrium.

hep-ph↗

arXiv2005

Production of quark pairs from classical gluon fields

We compute by numerical integration of the Dirac equation the number of quark-antiquark pairs produced in the classical color fields of colliding ultrarelativistic nuclei. Results for the dependence of the number of quarks on the strength of the background field, the quark mass and time are presented. We also perform several tests of our numerical method. While the number of qqbar pairs is parametrically suppressed in the coupling constant, we find that in this classical field model it could even be compatible with the thermal ratio to the number of gluons.

hep-ph↗

arXiv2005

Quark-antiquark production from classical fields and chemical equilibration

We compute by numerical integration of the Dirac equation the number of quark-antiquark pairs produced in the classical color fields of colliding ultrarelativistic nuclei. The backreaction of the created pairs on the color fields is not taken into account. While the number of qqbar pairs is parametrically suppressed in the coupling constant, we find that in this classical field model it could even be compatible with the thermal ratio to the number of gluons. After isotropization one could thus have quark-gluon plasma in chemical equilibrium.

hep-ph↗

arXiv2005

Non-perturbative plaquette in 3d pure SU(3)

We present a determination of the elementary plaquette and, after the subsequent ultraviolet subtractions, of the finite part of the gluon condensate, in lattice regularization in three-dimensional pure SU(3) gauge theory. Through a change of regularization scheme to MSbar and a matching back to full four-dimensional QCD, this result determines the first non-perturbative contribution in the weak-coupling expansion of hot QCD pressure.

hep-lat↗

arXiv2005

Quark-antiquark production from classical fields in heavy ion collisions: 1+1 dimensions

Classical color fields produced by the small-x wave functions of colliding ultrarelativistic nuclei have been numerically computed. We set up the framework for computing the production of small-mass quark-antiquark pairs in these color fields by numerically integrating the Dirac equation. This computation is essential for understanding the conversion of the initial gluonic state to chemically equilibrated quark-gluon plasma. To illustrate and overcome technical difficulties associated with the longitudinal dimension, we first consider numerically the case of one time + one longitudinal space dimension.

hep-ph↗

arXiv2004

Plaquette expectation value and gluon condensate in three dimensions

In three dimensions, the gluon condensate of pure SU(3) gauge theory has ultraviolet divergences up to 4-loop level only. By subtracting the corresponding terms from lattice measurements of the plaquette expectation value and extrapolating to the continuum limit, we extract the finite part of the gluon condensate in lattice regularization. Through a change of regularization scheme to MSbar and (inverse) dimensional reduction, this result would determine the first non-perturbative coefficient in the weak-coupling expansion of hot QCD pressure.

hep-lat↗

arXiv2004

Duality and scaling in 3-dimensional scalar electrodynamics

Three-dimensional scalar electrodynamics, with a local U(1) gauge symmetry, is believed to be dual to a scalar theory with a global U(1) symmetry, near the phase transition point. The conjectured duality leads to definite predictions for the scaling exponents of the gauge theory transition in the type II region, and allows thus to be scrutinized empirically. We review these predictions, and carry out numerical lattice Monte Carlo measurements to test them: a number of exponents, characterising the two phases as well as the transition point, are found to agree with expectations, supporting the conjecture. We explain why some others, like the exponent characterising the photon correlation length, appear to disagree with expectations, unless very large system sizes and the extreme vicinity of the transition point are considered. Finally, we remark that in the type I region the duality implies an interesting quantitative relationship between a magnetic flux tube and a 2-dimensional non-topological soliton.

hep-lat↗

arXiv2003

Four-loop vacuum energy density of the SU(N_c) + adjoint Higgs theory

We compute the dimensionally regularised four-loop vacuum energy density of the SU(N_c) gauge + adjoint Higgs theory, in the disordered phase. ``Scalarisation'', or reduction to a small set of master integrals of the type appearing in scalar field theories, is carried out in d dimensions, employing general partial integration identities through an algorithm developed by Laporta, while the remaining scalar integrals are evaluated in d = 3 - 2εdimensions, by expanding in ε<< 1 and evaluating a number of coefficients. The results have implications for the thermodynamics of finite temperature QCD, allowing to determine perturbative contributions of orders O(g^6 ln(1/g)), O(g^6) to the pressure, while the general methods are applicable also to studies of critical phenomena in QED-like statistical physics systems.

hep-ph↗

arXiv2003

The pressure of hot QCD up to g^6 ln(1/g)

The free energy density, or pressure, of QCD has at high temperatures an expansion in the coupling constant g, known so far up to order g^5. We compute here the last contribution which can be determined perturbatively, g^6 ln(1/g), by summing together results for the 4-loop vacuum energy densities of two different three-dimensional effective field theories. We also demonstrate that the inclusion of the new perturbative g^6 ln(1/g) terms, once they are summed together with the so far unknown perturbative and non-perturbative g^6 terms, could potentially extend the applicability of the coupling constant series down to surprisingly low temperatures.

hep-ph↗

arXiv2002

Four-loop logarithms in 3d gauge + Higgs theory

We discuss the logarithmic contributions to the vacuum energy density of the three-dimensional SU(3) + adjoint Higgs theory in its symmetric phase, and relate them to numerical Monte Carlo simulations. We also comment on the implications of these results for perturbative and non-perturbative determinations of the pressure of finite-temperature QCD.

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