Geometry and entanglement in the scattering matrix

Journal Article · 16 August 2021 · Annals of Physics

DOI: https://doi.org/10.1016/j.aop.2021.168581 · OSTI ID:1976822

Beane, Silas R. ^[1]; Farrell, Roland C.  ^[2]

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1. University of Washington, Seattle, WA (United States); OSTI
2. University of Washington, Seattle, WA (United States)

A formulation of nucleon–nucleon scattering is developed in which the S-matrix, rather than an effective-field theory (EFT) action, is the fundamental object. Spacetime plays no role in this description: the S-matrix is a trajectory that moves between RG fixed points in a compact theory space defined by unitarity. This theory space has a natural operator definition, and a geometric embedding of the unitarity constraints in four-dimensional Euclidean space yields a flat torus, which serves as the stage on which the S-matrix propagates. Trajectories with vanishing entanglement are special geodesics between RG fixed points on the flat torus, while entanglement is driven by an external potential. The system of equations describing S-matrix trajectories is in general complicated, however the very-low-energy S-matrix –that appears at leading-order in the EFT description– possesses a UV/IR conformal invariance which renders the system of equations integrable, and completely determines the potential. In this geometric viewpoint, inelasticity is in correspondence with the radius of a three-dimensional hyperbolic space whose two-dimensional boundary is the flat torus. This space has a singularity at vanishing radius, corresponding to maximal violation of unitarity. The trajectory on the flat torus boundary can be explicitly constructed from a bulk trajectory with a quantifiable error, providing a simple example of a holographic quantum error correcting code.

• Research Organization: University of Washington, Seattle, WA (United States)
• Sponsoring Organization: USDOE; USDOE Office of Science (SC)
• Grant/Contract Number: FG02-97ER41014; SC0020970
• OSTI ID: 1976822
• Journal Information: Annals of Physics, Journal Name: Annals of Physics Journal Issue: C Vol. 433; ISSN 0003-4916
• Publisher: ElsevierCopyright Statement
• Country of Publication: United States
• Language: English