” are reasonably nice expressions built on
the sigma-model fields and their derivatives, modulo the
-model classical equations of motion.
The sigma-model fields are typically matter fields
satisfy the pure spinor constraints
The conformal dimension of an operator is defined as the total number of derivatives, plus the number of .
The BRST operator , being a symmetry of the theory, acts on such expressions.
The ghost number of an operator is the total number of ’s minus the total number of .
is an operator
of the conformal dimension zero
and ghost number two, annihilated by
The gauge transformation
of the vertex operator is:
Unintegrated operators form the cohomology of the BRST operator
at the ghost number two.
This is, essentially, the Hilbert space of states in the worldsheet sigma-model
It is a fundamental principle of the string theory, that every state corresponds to some deformation of
the worldsheet theory. This leads to the concept of integrated vertex, which we will now describe.