This thesis studies U(1) Chern-Simons theory and its relation to the results of Chris Beasley and Edward Witten (2005). Using the partition function formalism, we are led to compare U(1) Chern-Simons theory as constructed by Manoliu (1998) to the results of Beasley and Witten (2005). This leads to an explicit calculation of the U(1) Chern Simons partition function on a closed Sasakian three-manifold and opens the door to studying rigorous extensions of this theory to more general gauge groups and three-manifold geometries.

This thesis studies U(1) Chern-Simons theory and its relation to the results of Chris Beasley and Edward Witten (2005). Using the partition function formalism, we are led to compare U(1) Chern-Simons theory as constructed by Manoliu (1998) to the results of Beasley and Witten (2005). This leads to an explicit calculation of the U(1) Chern Simons partition function on a closed Sasakian three-manifold and opens the door to studying rigorous extensions of this theory to more general gauge groups and three-manifold geometries.

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第17770号 / 理博第3893号 / 新制||理||1561(附属図書館) / 30577 / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)教授 青山 秀明, 教授 畑 浩之, 准教授 早田 次郎 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

We define hypersato structures: these structures admit three inequivalent Sasakian structures such that each of these structures shares a common Reeb vector field and a common contact form with the others two. It is interestingto notice that hypersato manifolds can be viewed as U(1) principal orbibundles with base space a 4n-dimensional hyperkahler orbifold. We also discuss some results on the moduli problem of these structures. / Definimos variedades hipersato: estas variedades admiten tres estructuras del tipo Sasaki inequivalentes de tal manera que estas tres estructuras poseen un campo vectorial del tipo Reeb y una forma de contacto en común. Variedades que admiten estructura hipersato pueden considerarse como espacios totales de un fibrado principal U(1) del tipo orbifold, donde el espacio base admite una métrica singular hiperkahler. Discutimos tambien algunos resultados acerca del espacio moduli de variedades admitiendo estas estructuras.