DRSN III: Supersymmetric Drift Geometry and the Spectral Master Operator (De Rerum Spectrale Natura, Report III, Version 2.0)

The drift deformation of Dirac operators introduced in the first report of this series (DSRN I,
DOI: 10.5281/zenodo.17873909) and extended to worldsheet–target coupling in DSRN II
(DOI: 10.5281/zenodo.17887608) provides a robust analytic framework for modifying lowerorder
geometric terms of Dirac-type operators while preserving domain, principal symbol and
spectrum. In this third report we construct the supersymmetric drift geometry, introducing
a drift deformation of worldsheet supercharges and coupling it to a drifted ten-dimensional
supersymmetric Dirac operator.
A bounded, self-adjoint generator
X = x ⊗ 1 + 1 ⊗ φ,
acting simultaneously on the worldsheet and target Hilbert spaces, produces the supersymmetric
spectral master operator
D(susy)
s = D(susy)
ws,s ⊗ 1 + Γws ⊗ D(10)
s .
We prove that this operator satisfies domain stability, self-adjointness, principal symbol
invariance and holomorphicity, and we establish an exact factorisation formula for its square,
leading to heat-kernel and Seeley–DeWitt coefficient factorisation. We further construct the
supersymmetric unified Spectral Action and show that supersymmetric conformal invariance
on the worldsheet, ten-dimensional spectral field equations and drift-stationarity of the master
operator are all equivalent to the single operator identity
[(D(susy)
s )2,X] = 0.
This establishes a unified operator-theoretic foundation for supersymmetric drift geometry
and prepares the ground for the drifted eleven-dimensional geometry developed in Report IV.