Intrinsic Bulk-Bulk Holography: Boundaryless Holographic Duality from Strictly Nearly Kähler Geometry and Modular Flow

The holographic principle, as formalized by the AdS/CFT correspondence, rests on two extrinsic geometric postulates: an asymptotic conformal boundary serving as an independent information carrier, and metric orthogonality between bulk gravitational and boundary field-theoretic degrees of freedom. While mathematically powerful, these assumptions cannot be naturally extended to closed boundaryless cosmological spacetimes, leaving a foundational gap in holographic descriptions of our universe. This work presents intrinsic bulk-bulk holography, a boundaryless realization of holographic duality grounded in the internal geometry of the compact 6-dimensional strictly nearly Kähler flag manifold SU(3)/T^2. Its tangent bundle admits a canonical 3+3 skew-dual decomposition TM = E ⊕ JE with everywhere nonvanishing cross-metric coupling g(E,JE) ≠ 0, induced by the intrinsic torsion ∇ J ≠ 0 of the nearly Kähler structure. This nonorthogonal geometric coupling acts as an endogenous UV–IR information channel connecting the macroscopic infrared gravitational sector (horizontal distribution E) and the microscopic ultraviolet gauge sector (vertical distribution JE), eliminating the need for artificial holographic boundaries. Tomita–Takesaki modular flow σ_t = Δⁱᵗ a Δ⁻ⁱᵗ, combined with the spectral inversion symmetry Λ ↔ -Λ of the modular operator, lifts this static skew-dual geometry into a fully dynamical holographic framework. In the low-energy infrared limit, skew cross-coupling is hierarchically suppressed, giving rise to emergent 4-dimensional Lorentzian spacetime with three macroscopic spatial directions from the horizontal distribution and one timelike direction from modular thermal time. The conventional AdS/CFT correspondence is recovered as a special limiting case under imposed boundary conditions, rather than constituting the fundamental definition of holography. The framework is unitary, self-contained, and free of external boundaries, providing a candidate geometric and algebraic substrate for a holographic principle applicable to closed cosmological spacetimes.