Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 20 (2024), 031, 27 pages      arXiv:2303.14181      https://doi.org/10.3842/SIGMA.2024.031

Transformations of Currents in Sigma-Models with Target Space Supersymmetry

Vinicius Bernardes a, Andrei Mikhailov b and Eggon Viana b
a) CEICO, Institute of Physics of the Czech Academy of Sciences, Na Slovance 2, 182 00 Prague 8, Czech Republic
b) Instituto de Fisica Teorica, Universidade Estadual Paulista, R. Dr. Bento Teobaldo Ferraz 271, Bloco II - Barra Funda, CEP:01140-070 - Sao Paulo, Brasil

Received April 19, 2023, in final form March 26, 2024; Published online April 10, 2024

Abstract
We develop a framework for 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.

Key words: sigma-models; conservation laws; anomalies; equivariant cohomology.

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