Transformations of Currents in Sigma-Models with Target Space Supersymmetry

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2024
• Main Authors: Bernardes, Vinicius, Mikhailov, Andrei, Viana, Eggon
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2024
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/212164
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Transformations of Currents in Sigma-Models with Target Space Supersymmetry. Vinicius Bernardes, Andrei Mikhailov and Eggon Viana. SIGMA 20 (2024), 031, 27 pages

We develop a framework for the systematic study of symmetry transformations of sigma-model currents in a special situation, when symmetries have a well-defined projection onto the target space. We then apply this formalism to pure spinor sigma-models, and describe the resulting geometric structures in the target space (which in our approach includes the pure spinor ghosts). We perform a detailed study of the transformation properties of currents, using the formalism of equivariant cohomology. We clarify the descent procedure for the ''universal'' deformation corresponding to changing the overall scale of the worldsheet action. We also study the contact terms in the OPE of BRST currents, and derive some relations between currents and vertex operators which perhaps have not been previously acknowledged. We also clarify the geometrical meaning of the ''minimalistic'' BV action for pure spinors in AdS.