Discreteness and integrality in 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...

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...

Conformal Field Theory and Graphs *

The ADE graphs – the root diagrams of the simply laced simple Lie algebras appeared in the framework of the two-dimensional conformal field theories (CFT) based on the affine algebra sl(2) k in the classification of modular invariant partition functions [1] and in some related lattice models [2]. The modular invariants are labelled by the Coxeter number h = k + 2 while their diagonal terms, enc...

Applied Conformal Field Theory