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

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.

References in corpus (5)

• 3+1 Formalism and Bases of Numerical Relativity
• Higher derivative corrections to black hole thermodynamics from supersymmetric matrix quantum mechanics
• The role of the geometric phases in adiabatic populations tracking for non-hermitian hamiltonians
• Adiabatic theorem for bipartite quantum systems in weak coupling limit
• Adiabatic transport of qubits around a black hole