BRST complex

We want to have some description similar to Eq. (32) for Maxwell.

In Type IIB the role of is played by the Ramond-Ramond bispinor superfield . In flat space one can think about as the product of left and right ’s:

(37)

(but there are no such things as and ).

As we explained, in Maxwell theory the superfield was interpreted as the generator of the ideal , more precisely of its “abelianization” . Is there a similar interpretation in Type IIB?

It turns out that in Type IIB the situation is more involved.

We will answer this question for Type IIB in and in flat space. We will find an interpretation of the Type IIB gauge invariant operators in terms of an ideal in some infinite-dimensional Lie superalgebra which we will call .

But:
  • will not be a quadratic Lie algebra

  • this interpretation will come with a puzzle