arXiv subjects

A. Rebhan

Publications and source records attributed to A. Rebhan.

At least 37 records · Page 2Linked to original sources

arXiv2004

Non-Fermi-Liquid Specific Heat of Normal Degenerate Quark Matter

We compute the low-temperature behavior of the specific heat of normal (non-color-superconducting) degenerate quark matter as well as that of an ultradegenerate electron gas. Long-range magnetic interactions lead to non-Fermi-liquid behavior with an anomalous leading $T\ln T^{-1}$ term. Depending on the thermodynamic potential used as starting point, this effect appears as a consequence of the logarithmic singularity in the fermion self-energy at the Fermi surface or directly as a contribution from the only weakly screened quasistatic magnetic gauge bosons. We show that a calculation of Boyanovsky and de Vega claiming the absence of a leading $T\ln T^{-1}$ term missed it by omitting vector boson contributions to the internal energy. Using a formulation which collects all nonanalytic contributions in bosonic ring diagrams, we systematically calculate corrections beyond the well-known leading-log approximation. The higher-order terms of the low-temperature expansion turn out to also involve fractional powers $T^{(3+2n)/3}$ and we explicitly determine their coefficients up to and including order $T^{7/3}$ as well as the subsequent logarithmically enhanced term $T^3 \ln (c/T)$. We derive also a hard-dense-loop resummed expression which contains the infinite series of anomalous terms to leading order in the coupling and which we evaluate numerically. At low temperatures, the resulting deviation of the specific heat from its value in naive perturbation theory is significant in the case of strongly coupled normal quark matter and thus of potential relevance for the cooling rates of (proto-)neutron stars with a quark matter component.

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arXiv2004

Anomalous specific heat in ultradegenerate QED and QCD

We discuss the origin of the anomalous $T\ln T^{-1}$ behavior of the low-temperature entropy and specific heat in ultradegenerate QED and QCD and report on a recent calculation which is complete to leading order in the coupling and which contains an infinite series of anomalous terms involving also fractional powers in $T$. This result involves dynamical hard-dense-loop resummation and interpolates between Debye screening effects at larger temperatures and non-Fermi-liquid behavior from only dynamically screened magnetic fields at low temperature.

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arXiv2004

A new anomalous contribution to the central charge of the N=2 monopole

We calculate the one-loop corrections to the mass and central charge of the BPS monopole in N=2 super-Yang-Mills theory in 3+1 dimensions using a supersymmetry-preserving version of dimensional regularization adapted to solitons. In the renormalization scheme where previous studies have indicated vanishing quantum corrections, we find nontrivial corrections that we identify as the 3+1 dimensional analogue of the anomaly in the conformal central charge of the N=1 supersymmetric kink in 1+1 dimensions. As in the latter case, the associated contribution to the ordinary central charge has exactly the required magnitude to preserve BPS saturation at the one-loop level. It also restores consistency of calculations involving sums over zero-point energies with the low-energy effective action of Seiberg and Witten.

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arXiv2004

Perturbative QCD at non-zero chemical potential: Comparison with the large-Nf limit and apparent convergence

The perturbative three-loop result for the thermodynamic potential of QCD at finite temperature and chemical potential as obtained in the framework of dimensional reduction is compared with the exact result in the limit of large flavor number. The apparent convergence of the former as well as possibilities for optimization are investigated. Corresponding optimized results for full QCD are given for the case of two massless quark flavors.

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arXiv2004

The Casimir effect for susy solitons

We discuss new insights into the quantum physics of solitons developed since 1997: why quantum corrections to the mass M and the central charge Z of solitons in supersymmetric (susy) field theories in 1+1 and 2+1 dimensions are nonvanishing, despite the fact that the zero-point energies of bosons and fermions seem to cancel each other, and the central charge is an integral of a total space derivative which naively seems to get contributions only from regions far removed from the soliton. Crucial are: (1) the requirement that the regularization scheme not only makes calculations finite, but it also should preserve (ordinary) supersymmetry, (2) the renormalization condition that tadpoles vanish in the trivial vacuum, (3) an anomaly in the central charge which is actually needed to saturate the Bogomolnyi bound, (4) the influence of the winding of classical fields on the quantum fields far away from the soliton.

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arXiv2003

Nonvanishing quantum corrections to the mass and central charge of the N=2 vortex and BPS saturation

The one-loop quantum corrections to the mass and central charge of the N=2 vortex in 2+1 dimensions are determined using supersymmetry-preserving dimensional regularization by dimensional reduction of the corresponding N=1 model with Fayet-Iliopoulos term in 3+1 dimensions. Both the mass and the central charge turn out to have nonvanishing one-loop corrections which however are equal and thus saturate the Bogomolnyi bound. We explain BPS saturation by standard multiplet shortening arguments, correcting a previous claim in the literature postulating the presence of a second degenerate short multiplet at the quantum level.

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arXiv2003

Anomalous specific heat in high-density QED and QCD

Long-range quasi-static gauge-boson interactions lead to anomalous (non-Fermi-liquid) behavior of the specific heat in the low-temperature limit of an electron or quark gas with a leading $T\ln T^{-1}$ term. We obtain perturbative results beyond the leading log approximation and find that dynamical screening gives rise to a low-temperature series involving also anomalous fractional powers $T^{(3+2n)/3}$. We determine their coefficients in perturbation theory up to and including order $T^{7/3}$ and compare with exact numerical results obtained in the large-$N_f$ limit of QED and QCD.

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arXiv2003

Gauge dependence identities for color superconducting QCD

Using generalized Nielsen identities a formal proof is given that the fermionic quasiparticle dispersion relations in a color superconductor are gauge independent. This turns out to involve gluonic tadpoles which are calculated to one-loop order in a two-flavor color superconductor. Regarding the appearance of gluon tadpoles, we argue that in QCD the color superconducting phase is automatically color neutral.

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arXiv2003

On the Apparent Convergence of Perturbative QCD at High Temperature

The successive perturbative estimates of the pressure of QCD at high temperature T show no sign of convergence, unless the coupling constant g is unrealistically small. Exploiting known results of an effective field theory which separates hard (order 2 pi T) and soft (order gT) contributions, we explore the accuracy of simple resummations which at a given loop order systematically treat hard contributions strictly perturbatively, but soft contributions without truncations. This turns out to improve significantly the two-loop and the three-loop results in that both remain below the ideal-gas value, and the degree of renormalization scale dependence decreases as one goes from two to three loop order, whereas it increases in the conventional perturbative results. Including the four-loop logarithms recently obtained by Kajantie et al., we find that this trend continues and that with a particular sublogarithmic constant the untruncated four-loop result is close to the three-loop result, which itself agrees well with available lattice results down to temperatures of about 2.5 T_c. We also investigate the possibility of optimization by using a variational (``screened'') perturbation theory in the effective theory. At two loops, this gives a result below the ideal gas value, and also closer to lattice results than the recent two-loop hard-thermal-loop-screened result of Andersen et al. While at three-loop order the gap equation of dimensionally reduced screened perturbation theory does not have a solution in QCD, this is remedied upon inclusion of the four-loop logarithms.

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arXiv2003

HTL quasiparticle models of deconfined QCD at finite chemical potential

Using quasiparticle models and imposing thermodynamic consistency, lattice data for the equation of state of deconfined QCD can be mapped to finite chemical potential. We consider a refinement of existing simple massive quasiparticle models using the non-local hard-thermal-loop (HTL) propagators, and certain NLO corrections thereof, to obtain the thermodynamic potential as a function of temperature and chemical potential. At small chemical potential we find that the results for the slope of constant pressure from our main model for 2 massless quark flavors is in good agreement with recent lattice data for 2+1 flavors while it deviates somewhat from lattice data for 2 flavors from another group. For zero temperature, we obtain an estimate for the critical chemical potential which is close to that obtained from simpler quasiparticle models.

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arXiv2003

Thermodynamics of the high-temperature quark-gluon plasma

We review the various methods which have been employed recently to describe the thermodynamics of the high temperature quark-gluon plasma using weak coupling techniques, and we compare their results with those of most recent lattice gauge calculations. Many of the difficulties encountered with perturbation theory at finite temperature are in fact not specific to QCD but are present in any field theory at finite temperature and will be discussed first in the simple example of the scalar field theory. We discuss the merits and limitations of various techniques which have been used to go beyond perturbation theory in the soft sector, such as dimensional reduction, screened perturbation theory or hard-thermal-loop perturbation theory, and Phi-derivable approximations. In the last part of the review, we focus on the later, which lead to a remarkably simple expression for the entropy of the quark-gluon plasma. When complemented with further, physically motivated, approximations, this approach reproduces accurately the entropy obtained from lattice gauge calculations at temperatures above 2.5 T_c, where T_c is the deconfinement temperature. This calculation thus provides also support to the physical picture of the quark-gluon plasma as a gas of weakly interacting quasiparticles.

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arXiv2002

Quantum corrections to the mass and central charge of solitons in 1+1 dimensions

We first discuss how the longstanding confusion in the literature concerning one-loop quantum corrections to 1+1 dimensional solitons has finally been resolved. Then we use 't Hooft and Veltman's dimensional regularization to compute the kink mass, and find that chiral domain wall fermions, induced by fermionic zero modes, lead to spontaneous parity violation and an anomalous contribution to the central charge such that the BPS bound becomes saturated. On the other hand, Siegel's dimensional reduction shifts this anomaly to the counter terms in the renormalized current multiplet. The superconformal anomaly is located in an evanescent counter term, and imposing supersymmetry, this counter term induces the same anomalous contribution to the central charge. Next we discuss a new regularization scheme: local mode regularization. The local energy density computed in this scheme satisfies the BPS equality (it is equal to the local central charge density). In an appendix we give a very detailed account of the DHN method to compute soliton masses applied to the supersymmetric kink.

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arXiv2002

Comment on `One Loop Renormalization of Soliton Quantum Mass Corrections in 1+1 Dimensional Scalar Field Theory Models' (Phys. Lett. B542 (2002) 282 [hep-th/0206047])

We refute the claim that previous works on the one-loop quantum mass of solitons had incorrectly dropped a surface term from a partial integration. Rather, the paper quoted in the title contains a fallacious derivation with two compensating errors. We also remark that the $ϕ^2\cos^2\ln(ϕ^2)$ model considered in that paper does not have solitons at the quantum level because at two-loop order the degeneracy of the vacua is lifted. This may be remedied, however, by a supersymmetric extension.

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arXiv2002

Renormalization Group Summation and the Free Energy of Hot QCD

Using an approach developed in the context of zero-temperature QCD to systematically sum higher order effects whose form is fixed by the renormalization group equation, we sum to all orders the leading log (LL) and next-to-leading log (NLL) contributions to the thermodynamic free energy in hot QCD. While the result varies considerably less with changes in the renormalization scale than does the purely perturbative result, a novel ambiguity arises which reflects the strong scheme dependence of thermal perturbation theory.

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arXiv2002

Comparing different hard-thermal-loop approaches to quark number susceptibilities

We compare our previously proposed hard-thermal-loop (HTL) resummed calculation of quark number susceptibilities using a self-consistent two-loop approximation to the quark density with a recent calculation of the same quantity at the one-loop level in a variant of HTL-screened perturbation theory. Besides pointing out conceptual problems with the latter approach, we show that it severely over-includes the leading-order interaction effects while including none of the plasmon term which after all is the reason to construct improved resummation schemes.

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arXiv2002

The anomaly in the central charge of the supersymmetric kink from dimensional regularization and reduction

We show that the anomalous contribution to the central charge of the 1+1-dimensional N=1 supersymmetric kink that is required for BPS saturation at the quantum level can be linked to an analogous term in the extra momentum operator of a 2+1-dimensional kink domain wall with spontaneous parity violation and chiral domain wall fermions. In the quantization of the domain wall, BPS saturation is preserved by nonvanishing quantum corrections to the momentum density in the extra space dimension. Dimensional reduction from 2+1 to 1+1 dimensions preserves the unbroken N=1/2 supersymmetry and turns these parity-violating contributions into the anomaly of the central charge of the supersymmetric kink. On the other hand, standard dimensional regularization by dimensional reduction from 1 to (1-epsilon) spatial dimensions, which also preserves supersymmetry, obtains the anomaly from an evanescent counterterm.

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arXiv2002

One-loop surface tensions of (supersymmetric) kink domain walls from dimensional regularization

We consider domain walls obtained by embedding the 1+1-dimensional $ϕ^4$-kink in higher dimensions. We show that a suitably adapted dimensional regularization method avoids the intricacies found in other regularization schemes in both supersymmetric and non-supersymmetric theories. This method allows us to calculate the one-loop quantum mass of kinks and surface tensions of kink domain walls in a very simple manner, yielding a compact d-dimensional formula which reproduces many of the previous results in the literature. Among the new results is the nontrivial one-loop correction to the surface tension of a 2+1 dimensional N=1 supersymmetric kink domain wall with chiral domain-wall fermions.

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arXiv2001

Hard thermal loops and QCD thermodynamics

These lectures give an introduction to thermal perturbation theory, hard thermal loops, and their use in a nonperturbative, approximately self-consistent resummation of the thermodynamical potentials of quantum chromodynamics.

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