Asymptotics with a cosmological constant: The solution space

Mao, Pujian

doi:10.1103/physrevd.99.104024

Cited by 14 publications

(20 citation statements)

References 58 publications

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“…To deal with low energy QCD, various theoretical approaches have been followed, e.g. Nambu-Jona-Lasinio (NJL)-like models [7][8][9][10][11][12][13][14][15][16][17][18][19], quark-meson models [20,21], chiral perturbation theory (ChPT) [22][23][24], path integral Hamiltonians [25,26], Effective Chiral Confinement Lagrangian approaches (ECCL) [27,28] and QCD sum rules (SRQCD) [29]. In addition, results for the light meson spectrum in the presence of background magnetic fields have been obtained from LQCD calculations [30][31][32][33][34][35].…”

Section: Introductionmentioning

confidence: 99%

Charged pion masses under strong magnetic fields in the NJL model

2018

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The behavior of charged and neutral pion masses in the presence of a static uniform magnetic field is studied in the framework of the two-flavor Nambu-Jona-Lasinio (NJL) model. Analytical calculations are carried out employing the Ritus eigenfunction method. Numerical results are obtained for definite model parameters, comparing the predictions of the model with present lattice QCD (LQCD) results.The study of the behavior of strongly interacting matter under intense external magnetic fields has gained increasing interest in the last few years, especially due to its applications to the analysis of relativistic heavy ion collisions and the description of compact objects like magnetars [1]. In this work we concentrate on the effect of an intense external magnetic field on π meson properties. This issue has been studied in the last years following various theoretical approaches for low-energy QCD, such as NJL-like models, chiral perturbation theory, path integral Hamiltonians and LQCD calculations (see e.g.[1] and refs therein). In the framework of the NJL model, mesons are usually described as quantum fluctuations in the random phase approximation (RPA) [2]. In the presence of a magnetic field, the corresponding calculations require some special care, due to the appearance of Schwinger phases [3] associated with quark propagators. For the neutral pion these phases cancel out, and as a consequence the usual momentum basis can be used to diagonalize the corresponding polarization function [4][5][6][7]. On the other hand, for charged pions Schwinger phases do not cancel, leading to a breakdown of translational invariance that prevents to proceed as in the neutral case. In this contribution we present a method based on the Ritus eigenfunction approach [8] to magnetized relativistic systems, which allows us to fully diagonalize the charged pion polarization function. Further details of this work can be found in Ref. [9].We start by considering the Euclidean Lagrangian density for the NJL two-flavor model in the presence of an electromagnetic field. One haswhere ψ = (u d) T , τ i are the Pauli matrices, and m 0 is the current quark mass, which is assumed to be equal for u and d quarks. The interaction between the fermions and the electromagnetic field A µ is driven by the covariant derivative D µ = ∂ µ − iQA µ whereQ = diag(q u , q d ), with q u = 2e/3 and q d = −e/3, e being the proton electric charge. We consider here an homogeneous stationary magnetic field along the 3 axis in the Landau gauge, A µ = B x 1 δ µ2 .

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Section: Introductionmentioning

confidence: 99%

Charged pion masses under strong magnetic fields in the NJL model

2018

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“…An interesting question is then how to extend the definition of Bondi mass, Bondi angular momentum and Bondi news in asymptotically locally de Sitter spacetimes, see e.g. [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. The approach that we will follow here is to gauge fix the gravitational field close to future null infinity in order to isolate the structure that generalizes the BMS 4 group [21,22] and its extension [23,24] to asymptotically locally de Sitter spacetimes.…”

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confidence: 99%

The $Λ$-BMS$_4$ group of dS$_4$ and new boundary conditions for AdS$_4$

Compère,

Fiorucci,

Ruzziconi

2019

Preprint

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Using the dictionary between Bondi and Fefferman-Graham gauges, we identify the analogues of the Bondi news, Bondi mass and Bondi angular momentum aspects at the boundary of generic asymptotically locally dS 4 spacetimes. We introduce the Λ-BMS 4 group as the residual symmetry group of Bondi gauge after boundary gauge fixing. This group consists in infinitedimensional non-abelian supertranslations and superrotations and it reduces in the asymptotically flat limit to the extended BMS 4 group. Furthermore, we present new boundary conditions for asymptotically locally AdS 4 spacetimes which admit R times the group of area-preserving diffeomorphisms as the asymptotic symmetry group. The boundary conditions amount to fix 2 components of the holographic stress-tensor while allowing 2 components of the boundary metric to fluctuate. They correspond to a deformation of a holographic CFT 3 which is coupled to a fluctuating spatial metric of fixed area.

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“…The analysis of the asymptotic structure of general relativity has also been extended to spacetimes which are asymptotically (A)dS 4 [63][64][65][66][67][68][69], where part of the motivations and intriguing questions pertain to the very nature, when Λ = 0, of gravitational radiation, mass, angular momentum, and news [70][71][72][73][74][75][76][77][78][79][80][81][82][83][84][85]. Even if there is no notion of S-matrix in this context, there are meaningful asymptotic symmetries and (yet poorly understood) memory effects.…”

Section: Motivationsmentioning

confidence: 99%

“…The Newman-Penrose (NP) formalism has been used by many authors to study BMS asymptotic symmetries and charges, and also to discuss the Newman-Unti gauge [82,127,128,136,161,162]. Here, after having studied the solution space in the partial Bondi gauge using the tensorial form of the Einstein equations, we turn to the NP formalism to study the evolution equations when the boundary sources β 0 and U A 0 are set to zero.…”

Section: Newman-penrose Formalism Weyl Scalars and Evolution Equationsmentioning

confidence: 99%

The partial Bondi gauge: Further enlarging the asymptotic structure of gravity

Geiller¹,

Zwikel²

2022

Preprint

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We present a detailed analysis of gravity in a partial Bondi gauge, where only the three conditions g rr = 0 = g rA are fixed. We relax in particular the so-called determinant condition on the transverse metric, which is only assumed to admit a polyhomogeneous radial expansion. This is sufficient in order to build the solution space, which here includes a cosmological constant, time-dependent sources in the boundary metric, logarithmic branches, and an extra trace mode at subleading order in the transverse metric. The evolution equations are studied using the Newman-Penrose formalism in terms of covariant functionals identified from the Weyl scalars, and we build the explicit dictionary between this formalism and the tensorial Einstein equations. This provides in particular a new derivation of the (A)dS mass loss formula. We then study the holographic renormalisation of the symplectic potential, and the transformation laws under residual asymptotic symmetries. The advantage of the partial Bondi gauge is that it allows to contrast and treat in a unified manner the Bondi-Sachs and Newman-Unti gauges, which can each be reached upon imposing a further specific gauge condition. The differential determinant condition leads to the Λ-BMSW gauge, while a differential condition on g ur leads to a generalized Newman-Unti gauge. This latter gives access to a new asymptotic symmetry which acts on the asymptotic shear and further extends the Λ-BMSW group by an extra abelian radial translation. This generalizes results which we have recently obtained in three dimensions.

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Asymptotics with a cosmological constant: The solution space

Cited by 14 publications

References 58 publications

Charged pion masses under strong magnetic fields in the NJL model

Charged pion masses under strong magnetic fields in the NJL model

The $Λ$-BMS$_4$ group of dS$_4$ and new boundary conditions for AdS$_4$

The partial Bondi gauge: Further enlarging the asymptotic structure of gravity

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