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• W3035210905 abstract "In this Thesis we study first- and second-quantized approaches describing $D=11$ supergravity using pure spinor variables. We introduce the so-called $D=11$ pure spinor superparticle through BRST cohomology arguments starting from the semi-light-cone gauge $D=11$ Brink-Schwarz-like superparticle. After performing a light-cone gauge analysis of the pure spinor BRST cohomology at ghost number three, we find the linearized equations of motion of $D=11$ supergravity in $D=9$ superspace. In addition, we construct a BRST-closed, ghost number one vertex operator made out of worldline fields and $D=11$ supergravity superfields, and we run into an inconsistency when constructing a ghost number zero vertex operator satisfying a standard descent equation. We then introduce the non-minimal version of the $D=11$ pure spinor superparticle, in which a composite $b$-ghost can be constructed satisfying ${Q,b} = P^{2}$. However, its complicated expression makes it difficult to check its nilpotency. We show that introducing an $SO(1,10)$ fermionic vector $bar{Sigma}^{a}$ simplifies the form of the $b$-ghost considerably, which allows us to verify that ${Q,b} = P^{2}$ and ${b,b}=$ BRST-exact. Using this $b$-ghost we propose an alternative ghost number zero vertex operator satisfying a standard descent equation. However, its expression will depend on non-minimal pure spinor variables in a very complicated fashion. After discussing this first-quantized approach for $D=11$ supergravity, we move on to discussing the pure spinor master actions introduced by Cederwall for studying maximally supersymmetric gauge theories. We show that these actions indeed describe $D=10$ super-Yang-Mills, $D=10$ super-Born-Infeld and $D=11$ supergravity by extracting the equations of motion in ordinary superspace for each one of these theories." @default.
• W3035210905 created "2020-06-19" @default.
• W3035210905 creator A5073082430 @default.
• W3035210905 date "2020-06-10" @default.
• W3035210905 modified "2023-09-27" @default.
• W3035210905 title "Pure spinors and $D=11$ supergravity" @default.
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