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

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

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

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

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

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

Regge spectrum

Reminder: the spectrum is obtained from

Assumptions

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

Chiral symmetry breaking

Example: soft wall model with positive-sign dilaton

After the replacement the spectrum is defined by

For the case in question (axial-vector mesons)

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.