Abstract
Abstract The transverse part of the vector-axial vector flavor current correlator in the presence of weak external electric field is studied using holography. The correlator is calculated using a bottom-up model proposed recently, that includes both contributions of higher string states and the non-linear dynamics of the chiral condensate. It is shown that for low momenta the result agrees with the relation proposed by Son and Yamamoto motivated by a simpler holographic model. This suggests that the Son-Yamamoto relation is generically valid in the IR of models with the proper chiral symmetry breaking pattern.
Highlights
Where Q is the electric charge matrix and ta are the flavor matrices
It is shown that for low momenta the result agrees with the relation proposed by Son and Yamamoto motivated by a simpler holographic model
In the first model the chiral symmetry breaking is done by appropriate IR boundary conditions, while in the second by the dynamics of the brane embedding in the higher dimensional space
Summary
We consider a system of Nf pairs of D4-branes - D4-antibranes in a fixed bulk gravitational background that describes the “glue”. The only nonzero field is the tachyon which diverges at the tip of the cigar As it is pointed out in [34] and [15], in case that the Nf quarks have the same mass the vacuum of the non abelian action consists of Nf copies of the abelian solution. This welcome physical feature is absent in the soft wall model, [21] It occurs here because the tachyon potential multiplies the full action and in particular the kinetic terms for the gauge fields, which couple to the chiral symmetry breaking vev. The rms error of numerical fits to spectra and decay constants is 10% − 15% In conclusion this simple bottom-up model, which is string theory inspired, incorporates many interesting QCD features
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