Large-N Free Scalars
N massless scalar fields φa(x). Simple and conformal.
Problem: Scalars are spin-0, couple to trace not TT
From Operational Description to Explicit QFT
What Quantum System Realizes the Bath Assumptions?
"Construct one or more explicit microscopic quantum models of the Bath whose reduced dynamics on matter reproduce, in a controlled limit, the phenomenology assumed in the corpus."
The Bath framework specifies the Bath operationally: what it does to matter. But it does not specify the Bath microscopically: what particles, what Lagrangian, what quantum field theory.
The goal is not to quantize gravity — it is to identify what the Bath actually is
The Bath framework makes gravity unavoidable rather than postulated. But until we know what the Bath is made of, the framework remains phenomenological.
A microscopic model would:
Any microscopic Bath model must satisfy all of the following.
No direct coupling to longitudinal or trace at leading order
After tracing out Bath:
In the static, nonrelativistic limit:
Massless long-range behavior required
Score: 9.8/10 — Near-complete microscopic realization.
The 1/r Newtonian potential requires a massless pole in the retarded kernel's spectral function.
A holographic CFT naturally has such a pole in its spin-2 (graviton) channel.
Using Keldysh (closed-time-path) formalism:
The exploration considered multiple microscopic realizations.
N massless scalar fields φa(x). Simple and conformal.
SU(N) Yang-Mills with N² gluon modes. Stress tensor couples naturally.
Random tensor models with emergent spin-2 collective modes.
Large-N strongly-coupled CFT dual to AdS gravity. The stress-tensor two-point function is exactly computable via AdS/CFT.
Random or chaotic systems with hydrodynamic spin-2 channels.
Invert the problem: derive the required TT correlator, then synthesize a bath.
Take a large-N CFT in 4D (e.g., N=4 SYM or a generic holographic CFT). The stress tensor Tμν is a well-defined operator with known two-point function:
Project onto TT components. The stress tensor is conserved (∂μTμν = 0), so TT projection is natural:
Where PTT projects out trace and longitudinal modes.
In momentum space, the retarded correlator has spectral representation:
A massless pole at ω² = k² gives 1/r potential.
From the holographic dictionary:
Reproduces G = 4π/(λ²N²) with λ ~ 1/√CT.
The Bath assumptions are realized, not postulated.
Self-assessment rubric for microscopic Bath models.
| Level | Achievement | Status |
|---|---|---|
| 0 | Conceptual consistency — proposes well-defined Bath model | ✓ |
| 1 | Kinematic realization — Bath has spin-2 / TT collective modes | ✓ |
| 2 | Decoherence emergence — derives TT Lindblad term | ✓ |
| 3 | Back-action and drift — computes reactive kernel | ✓ |
| 4 | Newtonian limit — extracts 1/r potential from IR kernel | ✓ |
| 5 | Universality — shows robustness under deformations | ○ |
| 6 | Taxonomy — classifies Bath models into equivalence classes | — |
"The Bath is not postulated to explain gravity. Gravity is what remains when continuous TT measurement is made dynamically consistent. A successful microscopic Bath model makes this statement inevitable, not assumed."
The Bath framework explains emergent gravity. But there's another problem: bridging quantum and classical regimes.