Electric Forces in the Charged SYK Model

TL;DR

This paper extends the understanding of force emergence in the charged SYK model, showing how electromagnetic forces arise alongside gravity through operator growth and momentum-size correspondence, linked to a Kaluza-Klein framework.

Contribution

It demonstrates how electric forces naturally emerge in the U(1)-invariant SYK model via mechanisms similar to gravitational force emergence, connecting charge units to Kaluza-Klein theory.

Findings

Electric forces arise through operator growth in the U(1)-SYK model.

The charge unit aligns with a Kaluza-Klein radius inverse.

The mechanisms mirror those responsible for gravitational force emergence.

Abstract

The connection between gravitational force and operator growth, reported in earlier papers, is generalized to include electromagnetic forces. It is shown how in the U(1)-invariant SYK system electric forces emerge through the same mechanisms -- the momentum-size correspondence, and operator growth -- that give rise to gravitational force. The unit of electric charge implied by the U(1)-SYK theory is consistent with a Kaluza-Klein radius inverse to the characteristic energy scale of the SYK theory.