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Holographic Models for Planar QCD without AdS/CFT Correspondence

Discussing holographic models for QCD using principles of AdS/CFT correspondence, focusing on the 5th coordinate and energy scales in the context of quark-hadron duality and chiral symmetry breaking.

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Holographic Models for Planar QCD without AdS/CFT Correspondence

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  1. Excited QCD 2010, February 3 (Tatra National Park, 2010) Holographic Models for Planar QCD without AdS/CFT Correspondence SergeyAfonin 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): YM theory on AdS boundary Type IIB string theory on in low-energy (i.e. supergravity) approximation in the limit String theory AdS/QCD correspondence – a program to implement such a duality for QCD following the principles of AdS/CFT correspondence Bottom up Up down We will discuss QCD The 5-th coordinate – (inverse) energy scale Equivalence of energy scales

  3. Main assumption of AdS/QCD: There is an approximate 5d holographic dual for QCD An important example of dual fields for the QCD operators: J Here

  4. 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 CSB - Ok where M is identified with the quark mass matrix and Σ with the quark condensate.

  5. 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

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

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

  8. 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

  9. Chiral symmetry breaking

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

  11. 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.

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