Workshops

The tt* equations I

70
reads

Martin Guest

2011-06-08
15:20:00 - 17:00:00

308 , Mathematics Research Center Building (ori. New Math. Bldg.)



Cecotti and Vafa introduced the equations of topological - antitopological fusion (tt* equations) for the ground state metrics of a family of supersymmetric quantum field theories (QFT). The equations were reformulated by Dubrovin as an integrable system (zero curvature equation). Cecotti and Vafa (On classification of N=2 supersymmetric theories, Comm. Math. Phys. 158 (1993) 569-644) predicted that "global" solutions of these equations are very restricted, and they used this to classify certain QFT of low Witten index. The mathematical aspects of these solutions are extremely rich, and, 20 years later, still not well understood. We shall try to explain the mathematical framework and give some sample results.