AdS QCD Model

8/13/2019 AdS QCD Model

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AdS/CFT CorrespondenceSoft Wall Model

Interaction of Scalar with two Pseudoscalar mesonsFinal Remarks

Interaction of Scalar Mesons in AdS/QCD

Soft Wall Model

Miguel Angel Martin Contreras

Department of PhysicsUniversidad de los Andes

Bogota, Colombia

2013

Miguel Angel Martin Contreras Interaction of Scalar Mesons in AdS/QCD Soft Wall Model
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Outline

1 AdS/CFT CorrespondenceAdS/CFT ConjectureHolographic DictionaryFrom AdS/CFT Correspondence to QCD

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Outline


2 Soft Wall ModelBuilding up the model


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Outline



3 Interaction of Scalar with two Pseudoscalar mesons3-Point Correlation Functions

Results


AdS/CFT C d
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Outline



3 Interaction of Scalar with two Pseudoscalar mesons3-Point Correlation FunctionsResults

4 Final RemarksConclusionsExpectations


AdS/CFT Correspondence
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AdS/CFT ConjectureHolographic DictionaryFrom AdS/CFT Correspondence to QCD

AdS/CFT Conjecture

eiAdS5

d4xO(x) 0(x)

|CFT =ei S5D[(x,z)]

|0; z0Miguel Angel Martin Contreras Interaction of Scalar Mesons in AdS/QCD Soft Wall Model

J. Maldacena, 1998.

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Definition

Bulk Side

Boundary Value of Bulk Field

(x, z) |z=0=0(x)

Bulk Masses m2Local Gauge Symmetry

IR Localized Field 0(x)

Kaluza Klein Tower

Boundary SideSource of CFT OperatorO

L =0(x)O

Dimension ofOGlobal Symmetry of CFT

CFT Bound State

Tower of Resonances

n=0d2n

p2+m2n

Calculation Rule

O (x1)O (x2) ...O (xn)CFT = nSon-shell5D [0,...]

0(x1) ...0(xn)

Sources=0

.


AdS/CFT CorrespondenceS/C C
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N= 4 SYM theory in(3 + 1)dimensions

Large Nc limit.

SUSY.

Conformal Symmetry.

All fields live in the adjointrepresentation of SU(Nc).

QCD

Nc= 3.

No SUSY.

Asymptotic Freedom.

Quarks in the fundamentalrepresentation of SU(3).


AdS/CFT CorrespondenceAdS/CFT C j t
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N= 4 SYM theory in(3 + 1)dimensions

Large Nc limit.

SUSY.

Conformal Symmetry.

All fields live in the adjointrepresentation of SU(Nc).

QCD

Nc= 3.

No SUSY.

Asymptotic Freedom.

Quarks in the fundamentalrepresentation of SU(3).

Desirable extensions of the Correspondence

1/Nc corrections: Relax large Nc limit

String theory instead SUGRA.

Breaking Conformal Symmetry and SUSYAdS deformations.Adding quarks in the fundamental representation.


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/ pSoft Wall Model


Building up the model

Central Idea

For a given AdS background (thermal or not), it is possible to induce a conformal

soft breaking (or deformation) using a smooth dilaton profile (z) =cnzn.


B. Battel, T. Gherghetta, 2008.

T. Gherghetta, N. Setzer, 2010.

G. Hailu, 2011.

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/ pSoft Wall Model


Building up the model

Central Idea

For a given AdS background (thermal or not), it is possible to induce a conformal

soft breaking (or deformation) using a smooth dilaton profile (z) =cnzn.

Let us consider the metric

dS2 =gMNdxM dxN =

R2

z2 e(z)dxdx +dz2

with z [0,], (z) =2 z2 and =diag(1, +1, +1, +1), as a solutionobtained from the general action

SSWM= 1

k d5x

g e [R+L

matter]

Here mediatesthe strength of the soft wall. For matter fields we will considerlight scalar mesons as a first approximation:

Lmatter=Tr

(D)

2

+m2

2

+

1

2g25F2

V+F2

A


B. Battel, T. Gherghetta, 2008.

T. Gherghetta, N. Setzer, 2010.

G. Hailu, 2011.

AdS/CFT CorrespondenceS f C
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Soft Wall ModelInteraction of Scalar with two Pseudoscalar mesons

Final Remarks

3-Point Correlation FunctionsResults

Definition

Scalar field: (x) = h2

+ T0

S0 +TaSa (x) e2i(x).

Covariant Derivative: D= d+i

AV1, iAA1 , .

Where a= 1, . . . , 8, a chiral field, h chiral order parameter, S0 a singlet and Sa

an octect of SU(3) respectively, the 1-form potentials given by FV,A2 = dAV,A1 ,

T0 =f(Nf) and Ta are the SU(3) generators.


AdS/CFT CorrespondenceS ft W ll M d l 3 P i t C l ti F ti
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Final Remarks


Definition

Scalar field: (x) = h2

+ T0

S0 +TaSa (x) e2i(x).

Covariant Derivative: D= d+i

AV1, iAA1 , .

Where a= 1, . . . , 8, a chiral field, h chiral order parameter, S0 a singlet and Sa

an octect of SU(3) respectively, the 1-form potentials given by FV,A2 = dAV,A1 ,

T0 =f(Nf) and Ta are the SU(3) generators.

The 3-point interaction for a scalar S and two pseudo scalars P is given by theexpansion of the D term:

SSPPeff =

4

k d5x

g e h (z) Tr S(d )2 Following the AdS/CFT Correspondence Recipe, the coupling constant gSnP P:

gSnPP=

Nc

4

m2Snf2

R,

0

dz e2z2 h (z)


AdS/CFT CorrespondenceSoft Wall Model 3 Point Correlation Functions
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Final Remarks


Results

gSnPP=

Nc

4

m2Snf2

R,

0

dz e2z2 h (z)

To obtain gSnPP, it is necessary to solve the e.o.m for the h field.

The value ofgSnPP is dependent of the scalar meson mass mSn .

Numerical results give gS0PP O (0, 1 GeV) for the lightest scalar meson f0.QCD estimates are near to 6 GeV (Pennington, 2001).


AdS/CFT CorrespondenceSoft Wall Model Conclusions
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Final Remarks

ConclusionsExpectations

Conclusions

gSnPPdepends linearly ofh (z), i.e., the quark condensate.

The origin of the small value for gSnPPcoupling in the soft wall model isrelated to the difficulty of correctly reproducing chiral symmetry breakingthrough the non vanishing chiral condensate h (z).


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Final Remarks


Things to to do next:

Chiral Symmetry Breaking (Witten-Sakai-Sugimoto approximation is an

example).Non-conformal extension.

Thermal extension.


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Final Remarks


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Documents

AdS QCD Model