Abstract
The D = 11 pure spinor superparticle has been shown to describe linearized D = 11supergravityinamanifestlycovariantway. Anumberofauthorshaveproposedthat its correlation functions be used to compute amplitudes. The use of the scalar structure of the eleven-dimensional pure spinor top cohomology introduces a natural measure for computing such correlation functions. This prescription requires the construction of ghost number one and zero vertex operators. In these notes, we construct explicitly a ghost number one vertex operator but show the incompatibiliy of a ghost number zero vertex operator satisfying a standard descent equation for D = 11 supergravity.
Highlights
A number of authors have proposed that its correlation functions be used to compute amplitudes
The use of the scalar structure of the eleven-dimensional pure spinor top cohomology introduces a natural measure for computing such correlation functions
This prescription requires the construction of ghost number one and zero vertex operators
Summary
The ghost number one vertex operator will be constructed from a small perturbation of the pure spinor BRST operator whose nilpotency will follow from the D = 11 linearized supergravity equations of motion and the pure spinor constraint. On the other hand, using eq (A.2) one can show that at linear order [DC , DD} = TCDADA − 2Ω[CD}ADA (3.4). Using the D = 11 supergravity constraints (A.12), one finds that. {Dα, Dβ} = (Γa)αβDa − 2Ω(αβ)γ Dγ if one defines the BRST operator to be (3.5). After converting (3.6) into a worldline vector with ghost number 1 by replacing operators by corresponding worldline fields, one concludes that. The linearized supercurvature components can be written in terms of the super spin-conection using eq (A.4).
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
