Symmetries of massless vertex operators in AdS(5) x S(5)

Abstract

The worldsheet sigma-model of the superstring in AdS(5) x S(5) has a one-parameter family of flat connections parametrized by the spectral parameter. The corresponding Wilson line is not BRST invariant for an open contour, because the BRST transformation leads to boundary terms. These boundary terms define a cohomological complex associated to the endpoint of the contour. We study the cohomology of this complex for Wilson lines in some infinite-dimensional representations. We find that for these representations the cohomology is nontrivial at the ghost number 2. This implies that it is possible to define a BRST invariant open Wilson line. The central point in the construction is the existence of massless vertex operators transforming exactly covariantly under the action of the global symmetry group. In flat space massless vertices transform covariantly only up to adding BRST exact terms. But in AdS we show that it is possible to define vertices so that they transform exactly covariantly.

LaTeX 54pp, v2: added explanations in Section 5; v3: added explanations, small corrections

References in corpus (7)

• Indices for Superconformal Field Theories in 3,5 and 6 Dimensions
• Superconformal Indices for $\mathcal{N}=6$ Chern Simons Theories
• Superstring Scattering Amplitudes with the Pure Spinor Formalism
• Simplifying and Extending the AdS_5xS^5 Pure Spinor Formalism
• Algebra of transfer-matrices and Yang-Baxter equations on the string worldsheet in AdS(5) x S(5)
• Perturbative study of the transfer matrix on the string worldsheet in AdS(5)xS(5)
• Baecklund transformations, energy shift and the plane wave limit

Cited by in corpus (22)

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• Cornering the unphysical vertex
• A construction of integrated vertex operator in the pure spinor sigma-model in AdS5xS5
• Finite dimensional vertex
• Quantum Current Algebra for the $Ad{S}_5\times S^5$ Superstring
• Yang-Baxter Deformations of the $Ad{S}_5\times S^5$ Pure Spinor Superstring
• A superfield realization of the integrated vertex operator in an $Ad{S}_5\times S^5$ background
• Worldsheet dilatation operator for the $AdS$ superstring
• Non-minimal fields of the pure spinor string in general curved backgrounds
• AdS pure spinor superstring in constant backgrounds
• Vertex operators for the plane wave pure spinor string
• BRST cohomology of the sum of two pure spinors
• Deformations, renormgroup, symmetries, AdS/CFT
• Vertex operators of ghost number three in Type IIB supergravity
• Supertwistor description of the $AdS$ pure spinor string
• Geometrical framework for picture changing operators in the pure spinor formalism
• Beta deformed sigma model and strong deformation coupling limit
• On worldsheet curvature coupling in pure spinor sigma-model
• Pure spinors in AdS and Lie algebra cohomology
• Ambitwistor pure spinor string in a type II supergravity background