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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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AdS/CFT CorrespondenceSoft Wall Model
Interaction of Scalar with two Pseudoscalar mesonsFinal Remarks
Outline
1 AdS/CFT CorrespondenceAdS/CFT ConjectureHolographic DictionaryFrom AdS/CFT Correspondence to QCD
Miguel Angel Martin Contreras Interaction of Scalar Mesons in AdS/QCD Soft Wall Model
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AdS/CFT CorrespondenceSoft Wall Model
Interaction of Scalar with two Pseudoscalar mesonsFinal Remarks
Outline
1 AdS/CFT CorrespondenceAdS/CFT ConjectureHolographic DictionaryFrom AdS/CFT Correspondence to QCD
2 Soft Wall ModelBuilding up the model
Miguel Angel Martin Contreras Interaction of Scalar Mesons in AdS/QCD Soft Wall Model
/
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AdS/CFT CorrespondenceSoft Wall Model
Interaction of Scalar with two Pseudoscalar mesonsFinal Remarks
Outline
1 AdS/CFT CorrespondenceAdS/CFT ConjectureHolographic DictionaryFrom AdS/CFT Correspondence to QCD
2 Soft Wall ModelBuilding up the model
3 Interaction of Scalar with two Pseudoscalar mesons3-Point Correlation Functions
Results
Miguel Angel Martin Contreras Interaction of Scalar Mesons in AdS/QCD Soft Wall Model
AdS/CFT C d
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AdS/CFT CorrespondenceSoft Wall Model
Interaction of Scalar with two Pseudoscalar mesonsFinal Remarks
Outline
1 AdS/CFT CorrespondenceAdS/CFT ConjectureHolographic DictionaryFrom AdS/CFT Correspondence to QCD
2 Soft Wall ModelBuilding up the model
3 Interaction of Scalar with two Pseudoscalar mesons3-Point Correlation FunctionsResults
4 Final RemarksConclusionsExpectations
Miguel Angel Martin Contreras Interaction of Scalar Mesons in AdS/QCD Soft Wall Model
AdS/CFT Correspondence
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AdS/CFT CorrespondenceSoft Wall Model
Interaction of Scalar with two Pseudoscalar mesonsFinal Remarks
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.
AdS/CFT Correspondence
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AdS/CFT CorrespondenceSoft Wall Model
Interaction of Scalar with two Pseudoscalar mesonsFinal Remarks
AdS/CFT ConjectureHolographic DictionaryFrom AdS/CFT Correspondence to QCD
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
.
Miguel Angel Martin Contreras Interaction of Scalar Mesons in AdS/QCD Soft Wall Model
AdS/CFT CorrespondenceS/C C
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AdS/CFT CorrespondenceSoft Wall Model
Interaction of Scalar with two Pseudoscalar mesonsFinal Remarks
AdS/CFT ConjectureHolographic DictionaryFrom AdS/CFT Correspondence to QCD
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).
Miguel Angel Martin Contreras Interaction of Scalar Mesons in AdS/QCD Soft Wall Model
AdS/CFT CorrespondenceAdS/CFT C j t
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AdS/CFT CorrespondenceSoft Wall Model
Interaction of Scalar with two Pseudoscalar mesonsFinal Remarks
AdS/CFT ConjectureHolographic DictionaryFrom AdS/CFT Correspondence to QCD
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.
Miguel Angel Martin Contreras Interaction of Scalar Mesons in AdS/QCD Soft Wall Model
AdS/CFT Correspondence
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/ pSoft Wall Model
Interaction of Scalar with two Pseudoscalar mesonsFinal Remarks
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.
Miguel Angel Martin Contreras Interaction of Scalar Mesons in AdS/QCD Soft Wall Model
B. Battel, T. Gherghetta, 2008.
T. Gherghetta, N. Setzer, 2010.
G. Hailu, 2011.
AdS/CFT Correspondence
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/ pSoft Wall Model
Interaction of Scalar with two Pseudoscalar mesonsFinal Remarks
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
Miguel Angel Martin Contreras Interaction of Scalar Mesons in AdS/QCD Soft Wall Model
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.
Miguel Angel Martin Contreras Interaction of Scalar Mesons in AdS/QCD Soft Wall Model
AdS/CFT CorrespondenceS ft W ll M d l 3 P i t C l ti F ti
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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.
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)
Miguel Angel Martin Contreras Interaction of Scalar Mesons in AdS/QCD Soft Wall Model
AdS/CFT CorrespondenceSoft Wall Model 3 Point Correlation Functions
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Soft Wall ModelInteraction of Scalar with two Pseudoscalar mesons
Final Remarks
3-Point Correlation FunctionsResults
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).
Miguel Angel Martin Contreras Interaction of Scalar Mesons in AdS/QCD Soft Wall Model
AdS/CFT CorrespondenceSoft Wall Model Conclusions
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Soft Wall ModelInteraction of Scalar with two Pseudoscalar mesons
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).
Miguel Angel Martin Contreras Interaction of Scalar Mesons in AdS/QCD Soft Wall Model
AdS/CFT CorrespondenceSoft Wall Model Conclusions
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Soft Wall ModelInteraction of Scalar with two Pseudoscalar mesons
Final Remarks
ConclusionsExpectations
Things to to do next:
Chiral Symmetry Breaking (Witten-Sakai-Sugimoto approximation is an
example).Non-conformal extension.
Thermal extension.
Miguel Angel Martin Contreras Interaction of Scalar Mesons in AdS/QCD Soft Wall Model
AdS/CFT CorrespondenceSoft Wall Model Conclusions
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Soft Wall ModelInteraction of Scalar with two Pseudoscalar mesons
Final Remarks
ConclusionsExpectations
Miguel Angel Martin Contreras Interaction of Scalar Mesons in AdS/QCD Soft Wall Model
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