Holographic cold nuclear matter as dilute instanton gas 1.Introduction 2.Model of Baryon system 3.D8 brane embedding 4.Chemical potential and phase transition (to nuclear matter) 5.Summary K. G, K. Kubo, M. Tachibana, T. Taminato, and F. Toyoda arXive; (2013)

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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 Strings

D4 stacked Background =D4 Soliton; (Witten) at the boundary (U  infinite) 4D Gauge Theory in confinement phase

2) Quarks and flavored mesons are introduced by 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 Ansatz Nf=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 function Most 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 ρ we 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 Transition E(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 = , 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