Mario Flory (Jagellonian U.) on Complexity and Conformal Field Theory

Abstract: We study circuit and state complexity in the universal setting of (1+1)-dimensional conformal ​ field theory and unitary transformations generated by the stress-energy tensor. We provide a unifi​ed view of assigning a cost to circuits based on the Fubini-Study metric, iteratively solve the emerging integro-diff​erential equation for sample optimal circuits and discuss the sectional curvature of the underlying geometry. We also discuss the relation of our work to Euler-Arnold type equations such as the Korteweg-de Vries and Hunter-Saxton equations.