Vector meson quasinormal modes in a finite-temperature AdS/QCD model
Luis A.H. Mamani
0
2
Alex S. Miranda
2
Henrique Boschi-Filho
1
Nelson R.F. Braga
1
0
Centro de Ciencias Naturais e Humanas, Universidade Federal do ABC
, Rua Santa Adelia 166, 09210-170, Santo Andre, SP,
Brazil
1
Instituto de Fsica, Universidade Federal do Rio de Janeiro
, Caixa Postal 68528, RJ 21941-972,
Brazil
2
Departamento de Ciencias Exatas e Tecnologicas, Universidade Estadual de Santa Cruz
, Rodovia Jorge Amado, km 16, 45662-900, Ilheus, BA,
Brazil
We study the spectrum of vector mesons in a finite temperature plasma. The plasma is holographically described by a black hole AdS/QCD model. We compute the boundary retarded Green's functions using AdS/CFT prescriptions. The corresponding thermal spectral functions show quasiparticle peaks at low temperatures. Then we calculate the quasinormal modes of vector mesons in the soft-wall black hole geometry and analyse their temperature and momentum dependences.
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Vector mesons in the soft-wall model at finite temperature
2.1 The soft-wall model
2.2 Equations of motion
2.3 The asymptotic wave functions
2.4 An analysis of the effective potentials
Contents
1 Introduction 2 3 4
The retarded Greens functions
3.1 Definitions and analytical results
3.2 Spectral functions at finite temperature
3.2.1 General procedure
3.2.2 Numerical results
Quasinormal modes
4.1 Perturbative analytical solutions
4.1.1 Longitudinal perturbations
4.1.2 Transverse perturbations
4.2 Numerical solutions
4.2.1 Power series method
4.2.2 Breit-Wigner resonance method
4.2.3 Numerical results
4.3 Dispersion relations
4.3.1 Longitudinal perturbations
4.3.2 Transverse perturbations 5
Conclusions
Introduction
Strong interactions are described by QCD. As it is well known, the coupling varies with the
energy. At high energies the coupling is small and the theory can be treated perturbatively
giving rise to the asymptotic freedom. At low energies perturbation theory does not work
and one needs alternative approaches. Gauge/string dualities provide an important tool
to study non perturbative aspects of strong interactions.
The connection between string and gauge theories started with the seminal work [1]
relating planar diagrams of non abelian gauge theories to string theory. More recently, a
remarkable duality between ten-dimensional string theory or eleven-dimensional M-theory
and a conformal gauge theory on the corresponding spacetime boundary was found in [2].
This so called AdS/CFT correspondence relates, in particular, string theory in AdS5 S5
space to four-dimensional SU(Nc) Yang-Mills gauge theory with large Nc and extended
N = 4 supersymmetry. String theory at low energies is described by a supergravity theory.
In this case, the AdS/CFT correspondence implies a gauge/gravity duality from which one
can calculate correlation functions for gauge-field operators [3, 4].
In this work we are interested in finite temperature properties of vector mesons. So,
we will consider the finite temperature version of the AdS/CFT correspondence in the
supergravity regime. This is obtained by considering a black hole embedded in an AdS
spacetime [5]. A prescription to calculate retarded propagators at finite temperature in the
gauge theory in Minkowski space was found in [6] (see also refs. [79]). This formulation
involves purely incoming-wave condition for the fields at the horizon, and such a condition
represents the total absorption by the black hole without any emission.
In the AdS/CFT correspondence the gauge theory is conformal. So, to describe strong
interactions one needs to break this symmetry. This is done in various phenomenological
models known as AdS/QCD where an infrared cut-off is introduced. An example is the
hard-wall model which introduces a hard cut-off on the bulk geometry [1012]. This model
was also studied at finite temperature for example in [13].
An alternative AdS/QCD model, that leads to linear Regge trajectories for vector
mesons and glueballs [1416], is the soft-wall model. In this case one introduces a scalar
field in the AdS geometry. This non uniform field works as a smooth infrared cut-off for
the dual gauge theory. The soft-wall model can also be considered at finite temperature.
In this case, there are two coexisting geometries, with and without a black hole. At high
temperatures the black hole geometry is (globally) stable, while the geometry without the
black hole is stable for low temperatures. The transition between these two regimes is a
Hawking-Page phase transition [17] and was studied for the soft-wall model in [18, 19].
We will study here the spectrum of vector mesons at finite temperature in the soft-wall
model considering, for all temperatures, a black hole embedded in the soft-wall background.
As discussed in [20], at intermediate and low temperatures this corresponds respectively
to the (supercooled) metastable and unstable phases of the plasma where the black hole is
still present. Studying the supercooled phase of the plasma (...truncated)