Axiomatic Conformal Field Theory

Operads and Conformal Field Theory Lecture 1: Conformal Field Theory

Physicists have developed very advanced methods to compute such integrals. For example, the famous Feynman diagram technique allows us to compute the above integral for a rather particular function S(x), a small perturbation of a positive de nite quadratic form in R . Sometimes, elaborate techniques of physicists to compute simple things nd an amazing application to very general things in mathe...

Axiomatic Topological Quantum Field Theory

This dissertation provides an introduction to the ideas employed in topological quantum field theory. We illustrate how the field began by considering knot invariants of three-manifolds and demonstrating the consequences of defining such a theory axiomatically. The ideas of category theory are introduced and we show that what we are actually concerned with are symmetric monoidal functors from t...

Beyond Conformal Field Theory

This is an account of some recent work done with H. S. La [1] [2], based ultimately on the work of Fischler and Susskind [3] and Polchinski [4]. Disciplines Physical Sciences and Mathematics | Physics This conference paper is available at ScholarlyCommons: http://repository.upenn.edu/physics_papers/548 Beyond Conformal Field Theory

Logarithmic Conformal Field Theory

The periods of arbitrary abelian forms on hyperelliptic Riemann surfaces, in particular the periods of the meromorphic Seiberg-Witten differential λ SW , are shown to be in one-to-one correspondence with the conformal blocks of correlation functions of the rational logarithmic conformal field theory with central charge c = c 2,1 = −2. The fields of this theory precisely simulate the branched do...

Applied Conformal Field Theory