Mathematical Foundations of Quantum Field Theory and Perturbative String Theory (Proceedings of Symposia in Pure Mathematics) (Proceedings of Symposia in Pure Mathematics, 83)

Conceptual progress in fundamental theoretical physics is linked with the search for the suitable mathematical structures that model the physical systems. Quantum field theory (QFT) has proven to be a rich source of ideas for mathematics for a long time. However, fundamental questions such as "What is a QFT?" did not have satisfactory mathematical answers, especially on spaces with arbitrary topology, fundamental for the formulation of perturbative string theory. This book contains a collection of papers highlighting the mathematical foundations of QFT and its relevance to perturbative string theory as well as the deep techniques that have been emerging in the last few years. The papers are organized under three main chapters: Foundations for Quantum Field Theory, Quantization of Field Theories, and Two-Dimensional Quantum Field Theories. An introduction, written by the editors, provides an overview of the main underlying themes that bind together the papers in the volume. Publisher's note Models for ([infinity symbol], n)-categories and the cobordism hypothesis / Julia Bergner From operads to dendroidal sets / Ittay Weiss Field theories with defects and the centre functor / Alexei Davydov, Liang Kong, and Ingo Runkel Homotopical poisson reduction of gauge theories / Frédéric Paugam Orientifold précis / Jacques Distler, Daniel Freed, and Gregory Moore Surface operators in 3d TFT and 2d rational CFT / Anton Kapustin and Natalia Saulina Conformal field theory and a new geometry / Liang Kong Collapsing conformal field theories, spaces with non-negative Ricci curvature and non-commutative geometry / Yan Soibelman Supersymmetric field theories and generalized cohomology / Stephan Stolz and Peter Teichner Topological modular forms and conformal nets / Christpher Douglas and André Henriques. Hisham Sati, Urs Schreiber, Editors. Includes Bibliographical References.