A superfield realization of the integrated vertex operator in an AdS 5 × S 5 background

Abstract

E-mail: ochandiaq@gmail.com, vallilo@gmail.com Abstract: The integrated massless vertex operator in an AdS 5 × S 5 background in the pure spinor formalism is constructed in terms of superfields.

General fluctuations of the heterotic pure spinor string on curved backgrounds

“…The calculation will be more involving because the absence of the (b, c) ghosts. However, the special cases of the superstring in a AdS 5 × S 5 background [9], [10] and its plane wave limit [16] were already studied, so the general background case can be performed.…”

“…This has been done for the AdS 5 × S 5 background in the pure spinor formalism. The unintegrated vertex was obtained in [8] and the integrated vertex operator was studied in [9] and [10]. What about other backgrounds or even a generic supergravity background?…”

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

“…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.…”

“…Note that an BRST-exact term is not allowed in the transformation of the integrated vertex operator because Q should act on a field with negative ghost number. This is not possible in the pure spinor formalism.This construction was explicitly done in [9] for the type II superstring in a flat background. We now consider our case.…”

Vertex operators for the plane wave pure spinor string

“…The scalar Φ is the field that changes the background value of the Ramond-Ramond flux by a constant amount [30,31]. However for E − = 0 it is not a scalar since it depends on the polarizations inside the functions (f a ,f a ).…”