Algebraic interpretation of SUGRA operators
There is a relation analogous to (13), namely exists an ideal such that:
This has an interesting consequence in the case when :
In particular, the linear space dual to :
describes gauge invariant local operators. The analysis of (28) is nontrivial, the only operator in AdS which I can identify is the dilaton where is some -invariant tensor and is defined in (37). In the flat space limit, the analysis simplifies:
We get the following equations of motion:
The gradient of the dilaton corresponds to , while does not have a clear interpretation in the Type IIB supergravity.
This rizes a question: do we correctly understand the low momentum sector of the Type IIB SUGRA? The pure spinor formalism suggests a different low momentum spectrum from what we all know from the textbooks. Is it possible that the textbooks miss some discrete degrees of freedom?
But we will now turn to a different subject. Let us look at what we can learn from the classical integrability of the worldsheet theory.