Equations of motion from Cederwall\u2019s pure spinor superspace actions

Nathan Berkovits,Max Guillen

doi:10.1007/jhep08(2018)033

Nathan Berkovits, Max Guillen

Open Access

https://doi.org/10.1007/jhep08(2018)033

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Abstract

Using non-minimal pure spinor superspace, Cederwall has constructed BRST-invariant actions for D = 10 super-Born-Infeld and D = 11 supergravity which are quartic in the superfields. But since the superfields have explicit dependence on the non-minimal pure spinor variables, it is non-trivial to show these actions correctly describe super-Born-Infeld and supergravity. In this paper, we expand solutions to the equations of motion from Cederwall’s actions to leading order around the linearized solutions and show that they correctly describe the interactions of D = 10 super-Born-Infeld and D = 11 supergravity.

Highlights

Motion correctly describe the usual on-shell D = 10 and D = 11 superfields which depend only on the superspace variables
An explicit procedure will be given for extracting the usual on-shell D = 10 and D = 11 superfields from the equations of motion of the pure spinor actions for the cases of D = supersymmetric Born-Infeld and for D = supergravity
This procedure will be given explicitly to first order in the coupling constant in these two actions, but it is expected that the procedure generalizes to all orders in the coupling constant as well as to other types of actions constructed from pure spinor superfields

Summary

Ten-dimensional pure spinor superparticle and super Yang-Mills

We will review the pure spinor description for the ten-dimensional superparticle and its connection with ten-dimensional super-Maxwell. One can show that the ten-dimensional super-Maxwell physical fields are described by ghost number one states: Ψ = λμAμ This can be seen since states in the cohomology satisfy the equation of motion and gauge invariance (γmnpqr)μν DμAν = 0 δAμ = DμΛ (2.3). These are the superspace constraints describing tendimensional super-Maxwell. Since the measure factor [dZ] picks out the top cohomology of the ten-dimensional pure spinor BRST operator, the transformation δΨ = QΛ is a symmetry of the action (2.4). Where [dZ] is the measure discussed above, Ψ is a Lie-algebra valued generic pure spinor superfield, Q is the non-minimal BRST operator and g is the coupling constant.

Physical operators

Eleven-dimensional pure spinor superparticle and supergravity

C Relation between Ψ and Φa