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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 interaction. 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. 2009-10-31 0910HIM-WCU 2

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Gluon dynamics is replaced by AdS5. Flavor dyn. By space filling branes. Meson=fluctuation of branes. 2009-10-31 0910HIM-WCU 4

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Global symmetry Boundary AdS/CFT gauge symmetry Bulk Local charge 2009-10-31 0910HIM-WCU 5

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Q=given baryon charge, q=parameter of RN BH relation of q & Q? 2009-10-31 0910HIM-WCU 6

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2009-10-31 0910HIM-WCU 7 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 2009-10-31 0910HIM-WCU 8

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2009-10-31 0910HIM-WCU 9 Z. Fodor, S.D. Katz Z. FodorS.D. Katz (hep-lat/0106002)

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With back reaction v.s Without 2009-10-31 0910HIM-WCU 1010 Main change is attributed to the def. change of T.

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2009-10-31 0910HIM-WCU 1212 Decay constants

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2009-10-31 0910HIM-WCU 1919 Pion mass rho mass BR-scaling is not there in bottom up approach. Caveat: coupling to the metric fluctuation is not included.

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Matter with probe brane 2009-10-31 0910HIM-WCU 2020

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2009-10-31 0910HIM-WCU 2121 Black D3 quark

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2009-10-31 0910HIM-WCU 2222 How mesons behave on this configuration?

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2009-10-31 0910HIM-WCU 2323 Gubser’s background Non supersymetric extension of D3-D(-1) bound system Supersymmetry and chiral symmetry is broken r 0 is proportional to the gluon condensation in gauge theory This geometry support confining phase

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Theoretical equipments are actions and eq. of M How D-branes vibrate : DBI 2009-10-31 0910HIM-WCU 2424

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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 2009-10-31 0910HIM-WCU 2525 Induced metric on D7 brane DBI action

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2009-10-31 0910HIM-WCU 2626 Equation of motion for Legendre transformed Hamiltonian

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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 distribution It is difficult. 2009-10-31 0910HIM-WCU 2929

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2009-10-31 0910HIM-WCU 3030 Baryons : D5 brane wrapped on an S 5 on which N c F1’s terminate 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 2009-10-31 0910HIM-WCU 3131 Dimensionless Displacement Equation of motion and solution Legendre transformed Hamiltonian

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2009-10-31 0910HIM-WCU 3232 D5 brane solution Force at cusp D4/D6(D3/D5) YS, S Sin, JHEP 0804:010, 2008

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2009-10-31 0910HIM-WCU 3333 Total configuration(Baryon D5 + F1’s +probe D7) can be stationary if there is force balance condition Force balance condition

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2009-10-31 0910HIM-WCU 3737 Deformation of D-brane Deformation of D5 braneBaryon mass Deformation of D7 braneBaryon-baryon interaction Density dependence of baryon mass mq = 1.5 mq = 1 mq =0 D4/D6(D3/D5) YS, S Sin, JHEP 0804:010, 2008

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2009-10-31 0910HIM-WCU 3838 Asymptotic behavior of D7 brane Chiral condensation

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Scalar fluctuation 2009-10-31 0910HIM-WCU 3939 Second order Lagranian with quardratic terms for fluctuation Equation of motion for fluctuation

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Effective potential 2009-10-31 0910HIM-WCU 4040

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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. 2009-10-31 0910HIM-WCU 4141

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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) 2009-10-31 0910HIM-WCU 4343

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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 ……. 2009-10-31 0910HIM-WCU 4444

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