Taming the 11D pure spinor b-ghost

Abstract

We provide an alternative compact expression for the 11D pure spinor b-ghost by introducing a new set of negative ghost number operators made out of non-minimal pure spinor variables. Using the algebraic properties satisfied by these operators, it will be straightforwardly shown that $$ \left\{Q,b\right\}=\frac{P^2}{2} $$ Q b = P 2 2 , as well as {b, b} = QΩ. As an application of this novel formulation, the ghost number two vertex operator will easily be obtained in a completely covariant manner from a standard descent relation, the ghost number three vertex operator will be shown to satisfy the generalized Siegel gauge condition, and the 11D supergravity two-particle superfield will be constructed in a quite simple way.

A Minimal b Ghost

“…The construction and examination of the b operator (mainly for D = 10 super-Yang-Mills theory and D = 11 supergravity) has been the subject of many papers, [9][10][11][12][13][14][15][16][17][18][19][20] mainly because this and similar issues is where the pure spinor superfield formalism becomes more complicated. In the present letter, we will work in D = 10 super-Yang-Mills theory, although analogous minimal operators should always exist.…”

“…The rewriting of the b operator in terms of physical operators in refs. [20,21] is probably one of the deepest and physically most meaningful ones. We expect it to hold equally in minimal variables.…”