Geometry and entanglement in the scattering matrix

• URL: http://arxiv.org/abs/2011.01278v2
• Date: Mon, 30 Aug 2021 16:59:47 GMT
• Title: Geometry and entanglement in the scattering matrix
• Authors: Silas R. Beane and Roland C. Farrell
• Abstract summary: A formulation of nucleon-nucleon scattering is developed in which the S-matrix is the fundamental object. The trajectory on the flat torus boundary can be explicitly constructed from a bulk trajectory with a quantifiable error.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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