Logarithmic Conformal Field Theory or how to Compute a Torus Amplitude on the Sphere
Abstract
We review some aspects of logarithmic conformal field theories which might shed some light on the geometrical meaning of logarithmic operators. We consider an approach, put forward by V. Knizhnik, where computation of correlation functions on higher genus Riemann surfaces can be replaced by computations on the sphere under certain circumstances. We show that this proposal naturally leads to logarithmic conformal field theories, when the additional vertex operator insertions, which simulate the branch points of a ramified covering of the sphere, are viewed as dynamical objects in the theory. We study the SeibergWitten solution of supersymmetric low energy effective field theory as an example where physically interesting quantities, the periods of a meromorphic oneform, can be effectively computed within this conformal field theory setting. We comment on the relation between correlation functions computed on the plane, but with insertions of twist fields, and torus vacuum amplitudes.
 Publication:

From Fields to Strings: Circumnavigating Theoretical Physics: Ian Kogan Memorial Collection (in 3 Vols). Edited by SHIFMAN MISHA ET AL. Published by World Scientific Publishing Co. Pte. Ltd
 Pub Date:
 2005
 DOI:
 10.1142/9789812775344_0029
 arXiv:
 arXiv:hepth/0407003
 Bibcode:
 2005ffsc.book.1201F
 Keywords:

 High Energy Physics  Theory
 EPrint:
 LaTeX, 38 pp. 3 figures (provided as eps and as pdf). Contribution to the Ian Kogan Memorial Volume "From Fields to Strings: Circumnavigating Theoretical Physics"