Geometry of Complexity in Conformal Field Theory
- URL: http://arxiv.org/abs/2005.02415v3
- Date: Wed, 27 Jan 2021 13:35:37 GMT
- Title: Geometry of Complexity in Conformal Field Theory
- Authors: Mario Flory and Michal P. Heller
- Abstract summary: We initiate quantitative studies of complexity in (1+1)-dimensional conformal field theories.
We embed Fubini-Study state complexity and direct counting of stress tensor insertion in relevant circuits in a unified mathematical language.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- 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.
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