General effective action for high-density quark matter

Abstract

We derive a general effective action for quark matter at nonzero temperature and/or nonzero density. For this purpose, we distinguish irrelevant from relevant quark modes, as well as hard from soft gluon modes by introducing two separate cut-offs in momentum space, one for quarks, Λq, and one for gluons, Λg. We exactly integrate out irrelevant quark modes and hard gluon modes in the functional integral representation of the QCD partition function. Depending on the specific choice for Λq and Λg, the resulting effective action contains well-known effective actions for hot and/or dense quark matter, for instance the "Hard Thermal Loop" or the "Hard Dense Loop" action, as well as the high-density effective theory proposed by Hong and others. We then apply our effective action to review the calculation of the color-superconducting gap parameter to subleading order in weak coupling, where the strong coupling constant g ≪ 1. In this situation, relevant quark modes are those within a layer of thickness 2Λq around the Fermi surface. The non-perturbative nature of the gap equation invalidates naive attempts to estimate the importance of the various contributions via power counting on the level of the effective action. Nevertheless, once the gap equation has been derived within a particular many-body approximation scheme, the cut-offs Λq, Λg provide the means to rigorously power count different contributions to the gap equation. We recover the previous result for the QCD gap parameter for the choice Λq < ∼ gµ ≪ Λg < ∼ µ, where µ is the quark chemical potential. We also point out how to improve this result beyond subleading order in weak coupling.

Black hole solution for scale-dependent gravitational couplings and the corresponding coupling flow

“…Since the classical form of (15) has been reproduced by various experiments at different scales, and since the special choice of c 4 allows to approximate very well to this result, it can be concluded that the solution (4) allows also for parameter choices which are also in agreement with current experimental limits and observations. The question to which extend observational data such as dark matter effects can be incorporated in the current solution (in the spirit of [54][55][56][57][58]) will be subject of future studies [59]. The above choice of parameters is most likely not the only one that achieves this goal, but the point is that it shows by construction that physically viable parameter choices are perfectly possible.…”

Exact renormalization group with optimal scale and its application to cosmology

“…In most existing studies [10,11,12,12], due the explicit choice of the functional form of k(x), one always had to sacrifice either general covariance (12), or the conservation of the stress energy tensor (13). In contrast to this, we propose to use the identity (14) in order to determine the relation between k and x ν .…”

“…In several analytical and numerical studies supporting evidence for this kind of scenario has been found [2,3,4,5,6,7,8,9]. In order to test the implications of this approach it has been studied in a large variety of contexts: Cosmology and Astrophysics [10,11,12,13,14,15,16], Brans Dicke theory [17], black holes [18,19,20,21,22], black holes in extra dimensions [23,24,25,26], interactions in extra dimensions [6], modified dispersion relations [27], f(R) gravity [28], deformed special relativity [29], and gravitational collapse [30]. This work contributes to the above studies in three ways:…”

Evolution of cosmological perturbations in a renormalization-group-driven inflationary scenario

“…where ξ is a O(1) parameter that is kept free for the time being. For the sake of completeness, it has to be pointed out that other choices are possible, as for exemple the cutoff k ∼ 1/t proposed in [24,26,28] or the k ∼ 1/a(t) in [29,30], while in [31][32][33] the cutoff dependence was adjusted to fit the energy-momentum conservation of ordinary matter.…”