Geometry of Complexity in Conformal Field Theory
Abstract
We initiate quantitative studies of complexity in (1+1)-dimensional conformal field theories with a view that they provide the simplest setting to find a gravity dual to complexity. Our work pursues a geometric understanding of complexity of conformal transformations and embeds Fubini-Study state complexity and direct counting of stress tensor insertion in the relevant circuits in a unified mathematical language. In the former case, we iteratively solve the emerging integro-differential equation for sample optimal circuits and discuss the sectional curvature of the underlying geometry. In the latter case, we recognize that optimal circuits are governed by Euler-Arnold type equations and discuss relevant results for three well-known equations of this type in the context of complexity.
Cite
@article{arxiv.2005.02415,
title = {Geometry of Complexity in Conformal Field Theory},
author = {Mario Flory and Michal P. Heller},
journal= {arXiv preprint arXiv:2005.02415},
year = {2021}
}
Comments
5+2 pages, an extended version is available as arXiv:2007.11555 v3: title change, added appendix, 1 figure