Pure spinors and $D=11$ supergravity

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.

arXiv comment158 pages, doctoral thesis

References in corpus (21)

• Super-Poincare Covariant Quantization of the Superstring
• Field Theory Without Feynman Diagrams: One-Loop Effective Actions
• Pure Spinor Formalism as an N=2 Topological String
• ICTP Lectures on Covariant Quantization of the Superstring
• The closed-string 3-loop amplitude and S-duality
• Towards Covariant Quantization of the Supermembrane
• Covariant One-Loop Amplitudes in D=11
• GAMMA: A Mathematica package for performing gamma-matrix algebra and Fierz transformations in arbitrary dimensions
• Multi-loop amplitudes in maximally supersymmetric pure spinor field theory
• Relating the Green-Schwarz and Pure Spinor Formalisms for the Superstring
• Supersymmetric Born-Infeld from the Pure Spinor Formalism of the Open Superstring
• Pure Spinor Vertex Operators in Siegel Gauge and Loop Amplitude Regularization
• Superstring Scattering Amplitudes with the Pure Spinor Formalism
• Pure spinor superfields -- an overview
• D=11 massless superparticle covariant quantization, pure spinor BRST charge and hidden symmetries
• Spinor moving frame, M0-brane covariant BRST quantization and intrinsic complexity of the pure spinor approach
• Equations of motion from Cederwall's pure spinor superspace actions
• Nilpotency of the b ghost in the non-minimal pure spinor formalism
• On the equivalence of the 11D pure spinor and Brink-Schwarz-like superparticle cohomologies
• Towards relating the kappa-symmetric and pure-spinor versions of the supermembrane
• Pure spinor indications of ultraviolet finiteness in D=4 maximal supergravity