My Ideal

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.