holographic cold nuclear matter as dilute instanton gas 1.introduction 2.model of baryon system 3.d8...
DESCRIPTION
1. Introduction based on Type IIA superstring : Quantum Gravity 4D SYM theory, etc 1) SU(Nc) Yang-Mills theory in confinement phase is dual to the 10D quantum gravity with stacked Nc D4 Branes ( BG = D4 soliton sol.) (=Large) Bulk Closed strings = Graviton Open StringsTRANSCRIPT
Holographic cold nuclear matteras dilute instanton gas
1. Introduction2. Model of Baryon system 3. D8 brane embedding4. Chemical potential and phase transition (to
nuclear matter)5. Summary
K. G, K. Kubo, M. Tachibana, T. Taminato, and F. Toyoda arXive; 1211.2499(2013)
写真• 1• 2
1. Introduction based on Type IIA superstring : Quantum Gravity 4D SYM theory, etc
1) SU(Nc) Yang-Mills theory in confinement phase is dual to the 10D quantum gravity with stacked Nc D4 Branes ( BG = D4 soliton sol.)
(=Large)
BulkClosed strings = Graviton
Open Strings
D4 stacked Background =D4 Soliton; (Witten)
at the boundary (U infinite)4D Gauge Theory in confinement phase
2) Quarks and flavored mesons are introducedby embedding flavor branes as probe ( Quenched Approxi.) Nf<<Nc
D8 Flavor branes
Color D4 branes
3) Baryons: The Baryon vertex is given by D4 brane wrapped on S^4 + Quarks which are given by Nc F Strings
Witten 1998
1) D8 DBI action ; world vol . = except for tau, Nf=2
2. Model of Baryon system in D8
Instanton Size ( and Position) is represented by
Gauge Fields are Solved under the following AnsatzNf=2 U(2) gauge
・ U(1) part = μ and n
SU(2) part=Instanton
Sum over many Instantons in dilute gas approxi.
,
(2) CS term D4(F_4)-D8[A_0-FF(instanton)] coupling
Here D4 is introduced as baryon source, then we obtain
total action for NI instantons (n-dep) is given as follows
Τ and ρ are remained to be solved
3. D8 embedding
1). Solution for Profile functionMost favorable simple anti-podal solution
Δx(D8-D8) >2πα’ for no tachyon
2) Ez or A0; chemical potential
the asymptotic solution of A0 is
4. Energy density and phase transition determination of ρwe define the energy (action) density as
where LQ is given as
we need a subtraction, which can be chosen as the energy density of the vacuum with n = 0. E(0)
thus estimate the energy difference for a given density n by
4.1 Phase TransitionE(μ(n)) − E(0) versus instanton size near phase transition point μcr ∼ 1.
fix the the value of ρ as ρm at the minimum of energy density, namely as Emin = E(ρm) for the given μ.
The phase transition, from vacuum to the nuclear matter phase at cr = 1.0176, is seen.
The diagram of (; n = 922 n) for the simple solution.
4.2 About the Size of baryon
and it is fitted by the curve
Strong Attraction
Dilute gas region
Dilute Gas OK
For GeV, we obtain near the critical point
Is normal density of nuclear
This density might be related to the inner density of neutron star
Summary and Discussion
In our model• Phase transition to a nuclear matter has been
found at finite charge density• The result is obtained within dilute gas
approximation• Rather High density is observed; possibility of core of neutron star