Half-BPS vertex operators of the AdS5 \xd7 S5 superstring

Nathan Berkovits

doi:10.1007/jhep07(2019)084

Abstract

Using the pure spinor formalism for the superstring in an AdS5 × S5 background, a simple expression is found for half-BPS vertex operators. At large radius, these vertex operators reduce to the usual supergravity vertex operators in a flat background. And at small radius, there is a natural conjecture for generalizing these vertex operators to non-BPS states.

Highlights

Using the pure spinor formalism for the superstring in an AdS5 × S5 background, a simple expression is found for half-BPS vertex operators
These vertex operators reduce to the usual supergravity vertex operators in a flat background
JHEP07(2019)084 were very recently proposed in [12] and will be shown here to be manifestly BRST-invariant and to closely resemble the vertex operators for Type IIB supergravity states in a flat background

Summary

Supergravity vertex operators

In any Type IIB supergravity background, the massless closed superstring vertex operator in unintegrated form in the pure spinor formalism is [13]. Where Aαβ are bispinor superfields depending on the N = 2B d = 10 superspace variables (xm, θLα, θRα ), α = 1 to 16 are Majorana-Weyl spinor indices, and λαL and λαR are left and right-moving pure spinor variables satisfying λLγmλL = λRγmλR = 0 for m = 0 to 9. The onshell equations of motion and gauge invariances are implied by QV = 0 and δV = QΩ where. ∇Lα and ∇Rα are the 32 fermionic covariant derivatives in the supergravity background. These equations of motion and gauge invariances imply that Aαβ satisfies γaαbγcde∇LαAγβ = γaαbβcde∇RαAγβ = 0, δAαβ = ∇LαΩRβ + ∇Rβ ΩLα,.

Flat background

Picture-changing

Half-BPS vertex operator

Explicit example

Summary