Can someone explain what are single-, double- and multi-trace operators are in AdS/CFT? I am a senior undergrad and only recently started studying AdS/CFT from TASI lectures and could not make much sense out of it. Could someone please explain it to a beginner with exhaustive details?
$\begingroup$
$\endgroup$
Add a comment
|
1 Answer
$\begingroup$
$\endgroup$
1
Briefly speaking, on the CFT boundary side of the holographic principle/AdS-CFT correspondence, there is a (super) YM theory with an $SU(N)$ color group. A boundary observable ${\cal O}(x)$ [build from color-matrix-valued fields] typically contains no external/unsummed/free color indices but instead [either a single or multiple] color-traces in order to be gauge-invariant.
-
$\begingroup$ Thanks for answering. So speaking crudely, if $\mathcal{O_1}(x)$ has a single color index, then $\text{tr}\,\mathcal{O}_1$ is a single-trace operator and $\mathcal{O}_2(x)$ has two colour indices, then with two color traces, it is a double-trace operator, correct? $\endgroup$ Commented Apr 11 at 7:02