Abstract
The construction of the ghost number zero and one vertex operators for the 11D pure spinor superparticle will be revisited. In this sense, an alternative way of defining the ghost number one vertex operator will be given after introducing a ghost number -2 operator made out of physical operators defined on the 11D non-minimal pure spinor superspace. This procedure will make explicit and transparent the relation between the ghost number three and one vertex operators. In addition, using a non-Lorentz covariant b-ghost, ghost number zero and two vertex operators satisfying standard descent equations will be presented in full form.
Highlights
An alternative way of defining the ghost number one vertex operator will be given after introducing a ghost number -2 operator made out of physical operators defined on the 11D non-minimal pure spinor superspace
We review the 11D pure spinor superparticle and its quantization in section 2. 11D physical operators are introduced in section 3, and an explicit map constructed out of them relating the ghost number three and one vertex operators is presented
One can readily see from eqs. (3.12)–(3.14) this ghost number one object is nothing but the ghost number one vertex operator (3.1) up to a BRST-exact term which can be ignored since it will decouple from any physical observable
Summary
The ghost number one vertex operator was constructed in [11] as a first order deformation to the BRST operator Q0 = λαdα in a flat background. Where hαa, hαβ are the deformations of Dα along the directions Dβ, ∂a, and Ωα βδ is the lowest-dimensional component of the super-spin-connection ΩA BC. One can show that U (1) is BRST-closed. It is invariant under super-gauge transformations up to BRST-exact terms. We will derive U (1) in (3.1) from the ghost number three vertex U (3) studied in section 2 through a ghost number -2 operator constructed out of non-minimal pure spinor variables
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