TL;DR
This paper introduces the modular Dirac equation to analyze and reconstruct spin 1/2 particles in nearly AdS2 spacetime, exploring symmetries and limitations of bulk reconstruction.
Contribution
It presents the modular Dirac equation, linking it to various mathematical structures and addressing challenges in bulk reconstruction with unknown couplings.
Findings
Properties of the modular Dirac operator are characterized.
Connections to the Schwarzian derivative and complex metrics are established.
Limitations of current bulk reconstruction methods are discussed.
Abstract
We introduce a new equation we dubbed the modular Dirac equation to see and reconstruct a spin 1/2 particle at the center of a nearly spacetime in the entanglement wedge reconstruction paradigm and we study hidden symmetries of this spacetime, too. Various properties of the Dirac modular operator are studied: a generalized Tomita-Takesaki construction, the connection to the Schwarzian derivative of the logarithm of the modular Dirac operator, the link with the an allowable complex metric, the connection to regenesis, we write the corresponding Lagrangian of the modular Dirac equation and we put in perspective some limitations of the current bulk reconstruction in the case of unknown couplings.
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