excited qcd 2010, february 3 (tatra national park, 2010)
DESCRIPTION
Excited QCD 2010, February 3 (Tatra National Park, 2010). Holographic Models for Planar QCD without AdS/CFT Correspondence. S ergey Afonin. Ruhr -University Bochum (Alexander von Humboldt Fellowship). Based on S.S. Afonin, arXiv : 1001.3105. A brief reminder. - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Excited QCD 2010, February 3 (Tatra National Park, 2010)](https://reader030.vdocuments.net/reader030/viewer/2022032605/56812bd7550346895d904420/html5/thumbnails/1.jpg)
Excited QCD 2010, February 3 (Tatra National Park, 2010)
Holographic Models for Planar QCD Holographic Models for Planar QCD without AdS/CFT Correspondencewithout AdS/CFT Correspondence
Sergey Afonin
Ruhr-University Bochum(Alexander von Humboldt Fellowship)
Based on S.S. Afonin, arXiv:1001.3105
![Page 2: Excited QCD 2010, February 3 (Tatra National Park, 2010)](https://reader030.vdocuments.net/reader030/viewer/2022032605/56812bd7550346895d904420/html5/thumbnails/2.jpg)
A brief reminder
AdS/CFT correspondence – the conjectured equivalence between a string theorydefined on one space and a CFT without gravity defined on conformal boundary ofthis space.
Maldacena example (1997):Type IIB string theory onin low-energy (i.e. supergravity)approximation
55AdS S
YM theory on AdS boundary4
in the limit 2 1YMg N
AdS/QCD correspondence – a program to implement such a duality for QCD following the principles of AdS/CFT correspondence
Up
dow
n
Bottom
up
String theory
QCD
We will discuss
(4, 2) :SO Equivalence of energy scales The 5-th coordinate – (inverse) energy scale
![Page 3: Excited QCD 2010, February 3 (Tatra National Park, 2010)](https://reader030.vdocuments.net/reader030/viewer/2022032605/56812bd7550346895d904420/html5/thumbnails/3.jpg)
![Page 4: Excited QCD 2010, February 3 (Tatra National Park, 2010)](https://reader030.vdocuments.net/reader030/viewer/2022032605/56812bd7550346895d904420/html5/thumbnails/4.jpg)
An important example of dual fields for the QCD operators:
Main assumption of AdS/QCD: There is an approximate 5d holographic dual for QCD
Here
J
![Page 5: Excited QCD 2010, February 3 (Tatra National Park, 2010)](https://reader030.vdocuments.net/reader030/viewer/2022032605/56812bd7550346895d904420/html5/thumbnails/5.jpg)
A typical model (Erlich et al., PRL 95, 261602 (2005))
For
Hard wall model:
The fifth coordinate corresponds to the energy scale:
Because of the conformal isometry of the AdS space, the running of the QCD gauge coupling is neglected until an infrared scale . At oneimposes certain gauge invariant boundary conditions on the fields.
Equation of motion for the scalar field
Solution independent of usual 4 space-time coordinates
where M is identified with the quark mass matrix and Σ with the quark condensate.
CSB - Ok
![Page 6: Excited QCD 2010, February 3 (Tatra National Park, 2010)](https://reader030.vdocuments.net/reader030/viewer/2022032605/56812bd7550346895d904420/html5/thumbnails/6.jpg)
Soft wall model (Karch et al., PRD 74, 015005 (2006))
The IR boundary condition is that the action is finite at
To have the Regge like spectrum:
To have AdS space in UV asymptotics:
The mesons of arbitrary spin can be considered, the spectrum is
2z
![Page 7: Excited QCD 2010, February 3 (Tatra National Park, 2010)](https://reader030.vdocuments.net/reader030/viewer/2022032605/56812bd7550346895d904420/html5/thumbnails/7.jpg)
![Page 8: Excited QCD 2010, February 3 (Tatra National Park, 2010)](https://reader030.vdocuments.net/reader030/viewer/2022032605/56812bd7550346895d904420/html5/thumbnails/8.jpg)
![Page 9: Excited QCD 2010, February 3 (Tatra National Park, 2010)](https://reader030.vdocuments.net/reader030/viewer/2022032605/56812bd7550346895d904420/html5/thumbnails/9.jpg)
![Page 10: Excited QCD 2010, February 3 (Tatra National Park, 2010)](https://reader030.vdocuments.net/reader030/viewer/2022032605/56812bd7550346895d904420/html5/thumbnails/10.jpg)
Let us substitute the expansion (17) into the action (11) and integrate over z
![Page 11: Excited QCD 2010, February 3 (Tatra National Park, 2010)](https://reader030.vdocuments.net/reader030/viewer/2022032605/56812bd7550346895d904420/html5/thumbnails/11.jpg)
![Page 12: Excited QCD 2010, February 3 (Tatra National Park, 2010)](https://reader030.vdocuments.net/reader030/viewer/2022032605/56812bd7550346895d904420/html5/thumbnails/12.jpg)
![Page 13: Excited QCD 2010, February 3 (Tatra National Park, 2010)](https://reader030.vdocuments.net/reader030/viewer/2022032605/56812bd7550346895d904420/html5/thumbnails/13.jpg)
Regge spectrum
Reminder: the spectrum is obtained from
Assumptions
![Page 14: Excited QCD 2010, February 3 (Tatra National Park, 2010)](https://reader030.vdocuments.net/reader030/viewer/2022032605/56812bd7550346895d904420/html5/thumbnails/14.jpg)
The most viable model
Requirements
1) Phenomenology:
2) Quark-hadron duality for J=1:
The only possibility – the soft wall model!
For positive-sign dilaton (except the scalars)
This coincide with the AdS/CFT prescription if we interpolate the meson states (except the scalars) by the lowest twist operators in QCD
and substitute their canonical dimension
into
![Page 15: Excited QCD 2010, February 3 (Tatra National Park, 2010)](https://reader030.vdocuments.net/reader030/viewer/2022032605/56812bd7550346895d904420/html5/thumbnails/15.jpg)
Chiral symmetry breaking
![Page 16: Excited QCD 2010, February 3 (Tatra National Park, 2010)](https://reader030.vdocuments.net/reader030/viewer/2022032605/56812bd7550346895d904420/html5/thumbnails/16.jpg)
![Page 17: Excited QCD 2010, February 3 (Tatra National Park, 2010)](https://reader030.vdocuments.net/reader030/viewer/2022032605/56812bd7550346895d904420/html5/thumbnails/17.jpg)
Example: soft wall model with positive-sign dilaton
After the replacement the spectrum is defined by
For the case in question (axial-vector mesons)
![Page 18: Excited QCD 2010, February 3 (Tatra National Park, 2010)](https://reader030.vdocuments.net/reader030/viewer/2022032605/56812bd7550346895d904420/html5/thumbnails/18.jpg)
Conclusions
• The holographic approach represents an alternative language for expressing the phenomenology of QCD sum rules in the large-N limit.
• The practical results of holographic models can be reproduced without use of the AdS/CFT prescriptions.
• The 4D ”visualization” of holographic CSB description leads to a natural emergence of the CSB scale and a natural degeneracy of highly excited vector and axial-vector mesons.