Wilson loops of Chern-Simons-matter Theories with one parameter and Picard-Fuchs equations

Abstract

Extending our previous work, we investigate Wilson loops of flavored Chern-Simons theory and ABJ theory by the use of Picard-Fuchs equations. The singularity structure of the equations is analyzed in detail, and local solutions around the singularities are determined. Each theory has one parameter, and the parameter dependence of the Wilson loops is also determined. In flavored Chern-Simons theory, we find an interesting phase transition. For $n$-times-wound Wilson loops, we determine their $n$-dependence by using a recursion relation obtained in our previous work.