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
:
| | | | |
| | modulo  |
| | |
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.
