1. Excited QCD 2010, February 3 (Tatra National Park, 2010) Holographic Models for Planar QCD without AdS/CFT Correspondence Sergey Afonin Ruhr-University Bochum (Alexander von Humboldt Fellowship) Based on S.S. Afonin, arXiv:1001.3105

2. A brief reminder AdS/CFT correspondence – the conjectured equivalence between a string theory defined on one space and a CFT without gravity defined on conformal boundary of this space. Maldacena example (1997): Type IIB string theory on in low-energy (i.e. supergravity) approximation YM theory on AdS boundary in the limit AdS/QCD correspondence – a program to implement such a duality for QCD following the principles of AdS/CFT correspondence Up down Bottom up String theory QCD We will discuss Equivalence of energy scales The 5-th coordinate – (inverse) energy scale

4. 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

5. 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 one imposes 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

6. 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

10. Let us substitute the expansion (17) into the action (11) and integrate over z

13. Regge spectrum Reminder: the spectrum is obtained from Assumptions

14. 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

15. Chiral symmetry breaking

17. Example: soft wall model with positive-sign dilaton After the replacement the spectrum is defined by For the case in question (axial-vector mesons)

18. 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.