Remarks on the two-dimensional power correction in the soft wall model

TL;DR

This paper derives the vector current correlator in the soft wall model via AdS/CFT, clarifies the coefficient of the two-dimensional power correction, and discusses its implications for the gluon condensate and scalar glueball correlator.

Contribution

It provides a direct derivation of the two-point correlator in the soft wall model and clarifies the value of the power correction coefficient, challenging previous string theory results.

Findings

The coefficient C_2 is found to be -c/2, not -c/3.

The gluon condensate is estimated to be approximately 0.064 GeV^4.

The two-dimensional correction cannot be eliminated by non-leading solutions in the bulk-to-boundary propagator.

Abstract

We present a direct derivation of the two-point correlation function of the vector current in the soft wall model by using the AdS/CFT dictionary. The resulting correlator is exactly the same as the one previously obtained from dispersion relation with the same spectral function as in this model. The coefficient $C_2$ of the two-dimensional power correction is found to be $C_2=-c/2$ with $c$ the slope of the Regge trajectory, rather than $C_2=-c/3$ derived from the strategy of first quantized string theory. Taking the slope of the $\rho$ trajectory $c\approx0.9{GeV}^2$ as input, we then get $C_2\approx-0.45{GeV}^2$. The gluon condensate is found to be $<\alpha_sG^2>\approx0.064{GeV}^4$, which is almost identical to the QCD sum rule estimation. By comparing these two equivalent derivation of the correlator of scalar glueball operator, we demonstrate that the two-dimensional correction can't be eliminated by including the non-leading solution in the bulk-to-boundary propagator, as was done in \cite{Colangelo2}. In other words, the two-dimensional correction does exist in the scalar glueball case. Also it is manifest by using the dispersion relation that the minus sign of gluon condensate and violation of the low energy theorem are related to the subtraction scheme.