A possible hint :

Following equations $2.5 \to 2.7$), we may define Kernels - Fourier transform of the $2$-point function - for the limiting cases ($f=0, f = +\infty$) :

$$G_{\pm}(k) \sim \int d^dk ~e^{ik.x} \frac{1}{x^{2 \Delta_\pm}}$$

We have then : $G_{\pm}(k) \sim ~ k^{\pm2\nu}$, where $\nu > 0$

We see, that in the UV, the kernel $G^+$ diverges, so it is not relevant in the UV, but converges in the IR. In the same manner, in the IR, the kernel $G^-$ diverges, so it is not relevant for the IR, but converges in the UV, so it would seem natural to associate the conformal dimension $\Delta^-$ ($f=0$), with the UV and the conformal dimension $\Delta^+$($f=+\infty$) with the IR.

We would have a RG flow which begins with $f=0$ in the UV, to finish at $f=+\infty$ in the IR

Finally, a list of the terms employed in the paper, which are not always clear:

$$\begin {matrix} UV & IR \\
f=0 & f=+\infty\\
"irregular" quantization & "regular" quantization\\
\Delta^- & \Delta^+\\
"irregular" boundary\, value & "regular" boundary \, value\\
\alpha = source & \beta = source\\
\beta = \langle O\rangle & \alpha = \langle O\rangle\\
\gamma = - \Delta^- &\gamma= + \infty\\
\end{matrix}$$

This post imported from StackExchange Physics at 2014-03-07 13:48 (UCT), posted by SE-user Trimok