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Holographic Heavy- Light mesons from non- Abelian DBI 　　

　Johanna Erdmenger, K. G, and Ingo Kirsch

ArXiv:0706.3978

近畿大 /07.08

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Contents:

1. Introduction

2. Specific BG and D7 branes embedding

3. D7s Fluctuations and HL mesons

Characteristic Properties of mass spectrum for various

vacuum

4. Summary

　

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1. Introduction

Approach 　 from AdS/CFT or string/gauge theory

non-perturbative QCD in IR

motivated by flavor quark with a definite mass introduced by D7 brane [Karch-Katz 　 02]

(1) Supersymmetric version 03

*AdS5 x S5 (N=4 SYM) [Karch-Katz, Kurczenski et al 03]

*Klebanov-Strassler BG [Sakai-Sonnenshein 03]

*Maldacena-Nunetz BG {Nunetz-Paredes-Ramallo 03] D5 is used

instead of D7

meson spectrum has been examined

by the fluctuations of probe brane

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(2) Non SUSY version;

Chiral symmetry breaking, Quark Confinement

IIA ; D4/D6 [KMMK], D4/D8[Sakai-Sugimoto 06] with KK modes,

IIB ; D3/D7 [Evans group, G-Y, .. 04]

(3) Finite Temperature version;

“Topology changing” Phase transition = melt down of mesons in the deconfinement phase

IIB ; D3/D7 [KMMK , Evans group, GSUY, ..]

(4) Chemical Potential version;

IIA ; D4/D8[Horigome-Tanii]

IIB ; D3/D7 [KMMMT, NSSY, our work is now preparing]

“Topology non-changing” unstable Phase transition

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(4) Present work is to study a system of H and L quarks by DBI

Paredes-Talavera 05, Evans-Erdmenger-Grosse 06, Bando-Sugamoto-Te

runuma 07, ..

By Polyakov or NG action

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2. BG (pure YM) and D7 branes embedding (quarks)

Type IIB Supergravity

(A)

(B)

Solution

and chiral symm breaking

pure YMLiu-Teytlin, ‘99, Kehagias-Sfetsos, ‘99

G-Yahiro, 04

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The meaning of the parameter q and from the dictionary

For non-susy sol.

The role of q quark confinining phase [Kehagias]

[K.G, M.Yahiro, hep-th/0408040]

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hep-th/9910053

+ ・・・

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Embedding : solve X profile function w

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For SUSY;

For non- SUSY;

Sol for w quark mass, chiral condensate, meson mass

For one brane

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3. D7s Fluctuations and HL mesons

and

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for

(for HL)

string connecting two branes

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For HL meson,

: ‘tHooft coupling constant

for n=l=0

A: SUSY sol

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compared to scalar

not dashed: scalar

at large mq: SUSY is restored

Deviate from scalar due to q

16too large

, grey: q=0

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Vectors

Higgs Mechanismmixing

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(+ gauge condensate )

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is not important in the spectrum

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6. Summary

1. 　 Holographic set up of HL mesons by non-Abelian DBI action, diagonal embedding

2. HL mesons have mass corr. to string connect. two separate branes // vector ; Higgs mechanism

scalar ;

3. then spectrum HH > HL for

4. For Heavy-quark

(i) spin effect vanishes (vector = scalar)

(ii) supuersymmetry is restored (spectrum degenerates)

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Bion ?

Survive at large λ

Energy of string connecting two branes

A condense