resting insights about the higher-dimensional conformal field theories as well as their gravitational duals.

[*Acknowledgments:*]{} We are thankful to A. Belitsky, S. Caron-Huot, A. Dymarsky, S. Hohennegger, E. Sokatchev for interesting discussions on this and related topics. We are especially grateful to G. Korchemsky and J. Maldacena for insightful discussions and comments on the manuscript. The work of AZ was supported in part by the US National Science Foundation under Grant No. PHY-0756966.

Here we explain equivalence of the detector definitions  and  using conformal transformation considered in . The transformation goes as follows where $y^{\pm} = y^0 \pm y^3$ and $x^{\pm} = x^0 \pm x^3$. Both large $r$ and $(x. \bar n)$ limits correspond to $x^+ \to \infty$ so that after the conformal transformation detectors are inserted at the null plane $y^+ = 0$. If we consider the contraction $T_{\mu \nu} \zeta^{\mu \nu}$ then after the transformation the polarization tensor takes the form The crucial point is that $ {\pa y^{+,1,2}  \over \pa x^{\mu}}|_{y^+ = 0} = 0$, so that after taking the limit arbitrary choice of the polarization tensor $\zeta^{\mu \nu}$ is related to the expectation value of $T_{--}(y^+=0,y^-,y^1,y^2)$. One can use this fact to argue that the energy and momentum flows in CFTs are related to each other as in theories with massless particles. The nonzero components take the form Thus, different choices of polarization tensors for detectors produce where we separated $\lim_{r \to \infty} r^2 (y^+)^2 = {1 \over (1 + n^3)^2}$ coming from the Jacobian $(y^+)^2$ which appears in addition to the change of polarization when we apply a conformal transformation to the primary field.

The detector choice of Hofman and Maldacena $T_{0 i} n^i$ produces if we consider instead $T_{\mu \nu} \bar n^{\mu} \bar n^{\nu}$ we get the factor $(n. \bar n)^2 = 4$ which explains an extra factor of ${1 \over 4}$ in  relative to . Another ${1\over 4}$ factor comes from $\lim_{(x. \bar n) \to \infty} (x.\bar n)^2 (y^+)^