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

Understand

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 $C_2\approx-0.45{GeV}^2$.