Fundamentals of the Pure Spinor Formalism (UvA-Proefschriften)

This thesis presents recent developments within the pure spinor formalism, which has simplified amplitude computations in perturbative string theory, especially when spacetime fermions are involved. Firstly the worldsheet action of both the minimal and the non-minimal pure spinor formalism is derived from first principles, i.e. from an action with two dimensional diffeomorphism and Weyl invariance. Secondly the decoupling of unphysical states in the minimal pure spinor formalism is proved. Joost Hoogeveen (1984) studied physics and mathematics, initially at the University of Amsterdam. In 2004 he continued these studies at the University of Cambridge. In 2005 he started his PhD research at the Institute of Theoretical Physics of the University of Amsterdam. Annotation This thesis presents recent developments within the pure spinor formalism, which has simplified amplitude computations in perturbative string theory, especially when spacetime fermions are involved. Firstly the worldsheet action of both the minimal and the non-minimal pure spinor formalism is derived from first principles, i.e. from an action with two dimensional diffeomorphism and Weyl invariance. Secondly the decoupling of unphysical states in the minimal pure spinor formalism is proved Contents......Page 8 Preface......Page 12 1. String theory......Page 14 2. Pure spinor formalism......Page 58 3. Basic techniques......Page 76 4. BRST quantisation of the pure spinor superstring......Page 98 5. Decoupling of unphysical states......Page 118 6. Discussion and conclusion......Page 156 Appendix A......Page 160 Bibliography......Page 168 Samenvatting......Page 174 Acknowledgments......Page 180