On the field-antifield (a)symmetry of the pure spinor superstring

Abstract

In this work, the DDF-like approach to the pure spinor cohomology is extended to the next ghost number level, the so called antifields. In a direct (supersymmetric) parallel to the bosonic string, some properties of the ghost number two cohomology are derived with the enlargement of the DDF algebra. Also, the DDF conjugates of the b ghost zero mode emerge naturally from the extended algebra and the physical state condition is discussed. Unlike the bosonic string case, the cohomology analysis of the pure spinor b ghost is restricted to BRST-closed states.

Connecting the ambitwistor and the sectorized heterotic strings

“…This can be checked, for example, by analyzing the eigenvalue with respect to the Lorentz generator M +− of the lowest component in the vector polarization. A similar issue was discussed in [23] in the context of the DDF-like description of antifields in the pure spinor formalism. It can be corrected by rescaling one of the polarizations by the momentum factor k, such that the correct vertex should be defined in terms ofĀȧ(ā k ,ξ, k) rather than Aȧ(a,ξ, k).…”

Relating the b ghost and the vertex operators of the pure spinor superstring

“…One important difference from [23] is that (1.1) is derived without using Lorenz gauge, just as in the bosonic string case. For discussions about the Siegel gauge in the context of pure spinor string see [26,27]. This work is organized as follows.…”

“…If we allow non-covariant descriptions there are even more possibilities. The paper [27] has a very interesting discussion on composite ghost fields and the relation between different descriptions of physical states in the context of DDF operators in the pure spinor string.…”

Vertex operators of ghost number three in Type IIB supergravity

“…Now suppose that F pq ; mn = 0. This implies that we can find Φ (4) , Φ (6) , Φ (8) and Φ (10) (all elements of M) satisfying:…”

“…(2) mn = 0 and therefore the existence of Φ (4) such that d L Φ (2) mn + δ L Φ (4) mn = 0. And so on until Φ (10) mn . Since Φ (10) mn is a top form, exists Ψ (9) ∈ M such that Φ 10 = d L Ψ (9) .…”