Operads, Strings And Deligne's Conjecture: A Text For Mathematicians And Physicists

Operads provide a universal language to relate several disciplines in mathematics and physics. The focus of this book, which is the first of its kind, is the particularly striking relation between algebra, topology and string theory that is mediated by operads of graphs and surfaces in their role as a model of the correlation functions of quantum field theory. The text supplies all the necessary background material, including discussions of the relevant aspects of operads, cell models, moduli spaces, deformation quantization, graph Feynman rules and topological and conformal field theory in their open/closed versions. The central paradigm is Deligne's conjecture on the Hochschild cohomology and its generalizations to the cyclic, the A and the moduli space cases. Its solution is presented as a natural consequence of this operadic point of view of strings.Starting at the basic definition and gradually proceeding to advanced topics at the forefront of research, the book provides the reader with a self-contained, uniform and natural approach to the subject which makes it a valuable resource for graduate students and researchers alike.