Emergent gravity and D-brane adiabatic dynamics: emergent Lorentz connection

TL;DR

This paper investigates how spacetime geometry, including Lorentz connection and torsion, emerges from quantum matrix models through adiabatic transport and Berry phase analysis of fermionic string states.

Contribution

It introduces a novel link between Berry phase generators and the Lorentz connection in emergent spacetime geometry within matrix theory.

Findings

The Lorentz connection emerges as the Berry phase generator.

Torsion appears at microscopic scales and influences the emergent geometry.

Berry curvature acts like a pseudo magnetic field in this context.

Abstract

We explore emergent geometry of the spacetime at the microscopic scale by adiabatic transport of a quasi-coherent state of a fermionic string, with quantum spacetime described by the matrix theory (BFSS matrix model). We show that the generator of the Berry phase is the shift vector of the spacetime foliation by spacelike surfaces associated with the quasi-coherent state. The operator-valued generator of the geometric phase of weak adiabatic transport is the Lorentz connection of the emergent geometry which is not torsion free at the microscopic scale. The effects of the torsion seem consistent with the usual interpretation of the Berry curvature as a pseudo magnetic field.