General fluctuations of the heterotic pure spinor string on curved backgrounds

Abstract

The general fluctuations, in the form of vertex operators, for the heterotic superstring in the pure spinor formalism are considered. The case of a flat background is reviewed and the case of a curved case is studied. The left-moving ghosts are pure spinors and the right-moving ghosts come from fixing the reparametrization invariance. The role of the reparametrization ghosts in the construction of the vertex operators is emphasized.

General fluctuations of the type II pure spinor string on curved backgrounds

“…It is interesting to note that if the fluctuation (5.3) is added to the world-sheet action (3.1) give a new supergravity background (linear in the fluctuations). Note that this was also the case for the heterotic string in a generic background [8]. The action becomes 12)…”

“…where F abγ = ∇ [a A b]γ and τ abc = γ αβ abc Ω α Ω β . Note this type of equation was obtained in [8] for the heterotic string in curved background. The solution of (4.7) is…”

“…The integrated vertex operator for type II superstring in a flat space-time background can be constructed in this manner and we review this in section 2. A similar construction was done in [9] for the AdS 5 × S 5 background, its plane-wave limit in [7] and for the heterotic string in a generic background in [8]. Our purpose is to generalize this result for the type II superstring in a generic supergravity background.…”

“…We could ask for the equivalent of U in non-flat backgrounds. This was done in [6] for the AdS 5 × S 5 background, its plane-wave limit in [7] and in for the heterotic string in [8] a generic background. Our goal is to study the case of type II in a generic supergravity background.…”