Taming the b antighost with Ramond-Ramond flux

Abstract

In the pure spinor formalism for the superstring, the b antighost is necessary for multiloop amplitude computations and is a composite operator constructed to satisfy {Q,b}=T where Q is the BRST operator and T is the holomorphic stress-tensor. In superstring backgrounds with only NS-NS fields turned on, or in flat space, one needs to introduce "non-minimal" variables in order to construct the b antighost. However, in Type II backgrounds where the Ramond-Ramond bispinor field-strength satisfies certain conditions, the b antighost can be constructed without the non-minimal variables. Although the b antighost in these backgrounds is not holomorphic, its antiholomorphic derivative is BRST-trivial. We discuss the properties of this operator both in the AdS_5 x S^5 background and in a generic curved background.

23 pages, harvmac; refs added; corrected the necessary conditions on Ramond-Ramond field to construct b antighost

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• Pure Spinor b-ghost in a Super-Maxwell Background
• A superfield realization of the integrated vertex operator in an $Ad{S}_5\times S^5$ background
• On Projections to the Pure Spinor Space
• A minimalistic pure spinor sigma-model in AdS
• Relating the $b$ ghost and the vertex operators of the pure spinor superstring
• Free Differential Algebras and Pure Spinor Action in IIB Superstring Sigma Models
• A Projection to the Pure Spinor Space
• Analytical solutions of pure-spinor superstring field theory
• On the Pure Spinor Heterotic Superstring $b$ Ghost
• Quantum corrections to $Ad{S}_5\times S^5$ left-invariant superstring current algebra