D2DFT · Defects in two dimensional field theories

The aim of this proposal is to study aspects of one dimensional defects in two dimensional field theories. One aspect is the relation of a certain class of defects, Wilson loops, to the integrable structure of Wess-Zumino-Witten models and coset models. Through the use of quantum groups, it should be possilbe to quantize these classical defects and describe exactly in a universal way a large class of boundary renormalization group flows of conformal field theories. A second aspect is the relations of defects to N=2 supersymmetric gauge theories in four dimensions. Recent results have shown mysterious connections between the eigenvalues of quantum defects and the instanton corrections of the moduli space of the gauge theories. We plan to study the defects of the Hitchin systems underlying the gauge theories, and relate them to kown defects in Liouville theory. This work should help elucidate the still poorly understood relations between N=2 gauge theories, integrable systems and conformal field theories in two dimensions.