A dual geometry of the hadron in dense matter

Abstract

We identify the dual geometry of the hadron phase of dense nuclear matter and investigate the confinement/deconfinement phase transition. We suggest that the low temperature phase of the RN black hole with the full backreaction of the bulk gauge field is described by the zero mass limit of the RN black hole with hard wall. We calculated the density dependence of critical temperature and found that the phase diagram closes. We also study the density dependence of the ρ meson mass. *

Properties of holographic mesons on dense medium

“…To work in confinement phase of dual boundary theory, we introduce a hardwall in the bulk, which makes the radial coordinate z to run from the boundary z = 0 to the hard wall z = z IR . It turns out that, within a hardwall formalism, tcAdS is more preferable to confinement in low density and low temperature regime than the usual extremal RN AdS black hole [19]. The resulting tcAdS solution merely takes the form of the zero-temperature limit of the RN AdS black hole of vanishing mass with the inserted hardwall, which hides a naked singularity.…”

“…Then, the well-known solution is given by ReissnerNordstrom AdS (RN AdS) black hole, from which thermal charged AdS(tcAdS) space can be constructed to study confining phase of the dense medium at zero temperature, which is nothing but RN AdS black hole of vanishing mass with a hard-wall [19]. The inserted hard-wall plays a role of setting up an infrared cutoff of the dual boundary theory in the confining phase and, at the same time, prevents any harm to bulk quantities from the naked singularity.…”

“…Moreover, after an appropriate holographic renormalization, to guarantee the well-defined Legendre transformation of the thermodynamic energies [19,20,23,25] leads to the relation,…”

“…At this stage of the Lagrangian to the quadratic order, there exist mixing terms between the axial-vector a i µ and the pseudoscalar π i , which can be removed by decomposing the axial-vector field into the transverse pieceā i µ and the longitudinal piece such as [4] 19) subject to the divergenceless condition ∂ µā i µ = 0. As in [17]…”

“…These works can be further generalized to the bottom-up models on dense medium [17][18][19][20][21][22][23][24][25][26][27][28]. The density in the dual boundary field theory implies to introduce a U (1) gauge…”