To be or not to be, BR-scaling in hQCD

Sang-Jin Sin (HYU) @him-wcu 09.10

To be or not to be, BR-scaling in hQCD

Sang-Jin Sin (HYU) @him-wcu 09.10

With Y. Seo, J.P. Shock, D. Zoakos(0911.xxxx)

CY.Park, KH. Jo, BH Lee(0909.3914 )

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A good way summarizing the effect of the in-teraction.

Brown and Rho: m* goes lower. Based on tendency near chiral restoration. C14 and other remarkable applications. Yet. No observable support. Lattice calculation with density is still difficult.

So, need new idea.

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Introduction: Dynamical mass*

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AdS/CFT

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Gluon dynamics is replaced by AdS5.

Flavor dyn. By space filling branes.

Meson=fluctuation of branes.

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Bottom Up Approach

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Global symme-try

Boundary

AdS/CFT

gauge symme-try

Bulk

Local charge

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Baryon Chemical potential

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Q=given baryon charge, q=parameter of RN BH

relation of q & Q?

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Coupling of (metric + vector)

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Result: AdS charged black hole

Chamblin et.al hep-th/9902170: with Q asR charge

Here It is consequence of the back reaction and Q=baryon charge

Remark: this is for deconfined phase.

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Dual to MIT bag-Model

In/Out is switched in ads/cft

Cut off r >r_m

Use z=1/r

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Hardwall and confinement

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Phase diagram: fixed chemical potential

Z. Fodor, S.D. Katz (hep-lat/0106002)

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With back reaction v.s Without

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Phase diagram (fixed density)

Main change is attributed to the def. change of T.

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Confining Phase with Baryon charge

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Eq.of M & B.C

Decay constants

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Vector meson in medium

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a1 vs density

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Pion decay constant

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Pion velocity vs density

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Pion mass vs density

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Summary: Bottom up. I

Pion mass

rho mass

BR-scaling is not there in bottom up approach.

Caveat: coupling to the metric fluctua-tion is not included.

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Matter with probe brane

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Top Down Approach

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Chemical potential with quark

Black D3

quark

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Chemical potential with Baryon

How mesons behave on this configu-ration?

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Background geometry

Gubser’s background

Non supersymetric extension of D3-D(-1) bound system

Supersymmetry and chiral symmetry is broken

r0 is proportional to the gluon condensation in gauge the-ory

This geometry support confining phase

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Theoretical equipments are actions and eq. of M

How D-branes vibrate : DBI

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Hardwares: DBI action

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We consider D7 brane as a probe brane where the other end point of fundamental strings are attached

End point can be regarded as point source on D7 brane

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Probe D7 brane: action

Induced metric on D7 brane

DBI action

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D7: first integral and Ruthian Equation of motion for

Legendre transformed Hamiltonian

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D7 embedding

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Ex: Chiral condensation and m_q

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For dense matter we need D5.

Add baryon vertices in uniform fashion along

D3 direction (spacial direction).

Remark: For single or non-uniform density distributionIt is difficult.

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D5

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DBI for D5 (Baryon vertex)

Baryons : D5 brane wrapped on an S5 on which Nc F1’s termi-nate The background 5-form field strength can couple to the world volume U(1) gauge field via Chern-Simons term

DBI action for single D5 brane with Nc F1’s

Induced metric on D5 brane

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ν Nc F1’s are attached at south pole and (1- ν)Nc F1’s at north pole

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Eq. of M for D5 Dimensionless Displacement

Equation of motion and solution

Legendre transformed Hamiltonian

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Shape of Baryon vertex D5 brane solution

Force at cusp

D4/D6(D3/D5) YS, S Sin, JHEP 0804:010, 2008

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Interaction of D7-D5:force balance with Baryon vertex Total configuration(Baryon D5 + F1’s +probe D7) can be sta-

tionary if there is force balance condition Force balance condition

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Fixed Q, varing m_q

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Baryon mass with density Deformation of D-brane

Deformation of D5 brane Baryon mass

Deformation of D7 brane Baryon-baryon interaction

Density dependence of baryon mass

mq = 1.5mq = 1mq =0

D4/D6(D3/D5) YS, S Sin, JHEP 0804:010, 2008

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Chiral condensation in Medium

Asymptotic behavior of D7 brane

Chiral condensation

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Scalar fluctuation

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Meson: Fluctuation on D7 brane

Second order Lagranian with quardratic terms for fluctua-tion

Equation of motion for fluctuation

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Effective potential

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Fluctuation on D7 brane

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By using shooting method, we can calculate mass spectrum of fluctuation, which is meson.

For large enough quark mass, meson mass decreases!

In such case BR-scaling exist.

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Fluctuation on D7 brane

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For very small m_q:

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BR scaling is possible for some model for appreciable quark mass, while it is not there in some of the model.

Remark: So are we are still in pion mode. Vector mode will be reported in future. (Rho Seo SJS)

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Summary

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Here, we studied Density dependences.

Following objects are calculable in hqcd: 0.Phase diagram (not critical point/crossover). 1. equation of state. 2. all Thermodnamic quantities. 3. condensations (chiral , gluon, meson … ) 4. susceptiblities. compressibility 5. spectral functions. 6. Symmetry energies. 7. Differnet models and Different modes. Etc …….

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Conclusion: What next?