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 (CFT) has proven to be one of the richest and deepest subjects of modern theoretical and mathematical physics research, especially as regards statistical mechanics and string theory. It has also stimulated an enormous amount of activity in mathematics, shaping and building bridges between seemingly disparate fields through the study of vertex operator algebras, a (partial...

Boundary conformal field theory (BCFT) is simply the study of conformal field theory (CFT) in domains with a boundary. It gains its significance because, in some ways, it is mathematically simpler: the algebraic and geometric structures of CFT appear in a more straightforward manner; and because it has important applications: in string theory in the physics of open strings and D-branes, and in ...

The string theory is a fast moving subject, both physics wise and in the respect of mathematics. In order to keep up with the discipline it is important to move with new ideas which are being stressed. Here I wish to give extracts from new papers of ideas which I have recently found interesting. There are six papers which are involved: I ."Strings formulated directly in 4 dimensions " A. N...

Convergence and analytic extension are of fundamental importance in the mathematical construction study conformal field theory. The author reviews some main convergence results, conjectures problems theories using representation theory vertex operator algebras. He also related problems. discusses extensions products intertwining operators (chiral fields) q-traces pseudo-q-traces operators. resu...