Black Hole Microstates as (E8)₁ CFT States — Closing the Sakharov–Jacobson Circle via the E8 Root Lattice

We identify the microstates of a Schwarzschild horizon as states of the chiral CFT (E8)₁ living on the horizon, counted by the Cardy formula with central charge c = 248/(1+30) = 8. This reframes the failure of naive lattice counting (ln 248 ≈ 5.51 per Planck cell, a factor ~22 too large) as a violation of the holographic principle — bulk counting gives S ~ V instead of S ~ A — and the 248 generators of E8 reappear correctly placed as the first excited level d(1) = 248 of the WZW character E4/η⁸ (1, 248, 4124, 34752, …). The algebraic identity 1/4 = (1+3)/(2·rk E8) connects the split-octonionic reduction O = 1+3+4 (which produces d = 4 with Lorentzian signature — a property D8 and A8 lack) with Wolfson's geometric derivation of the Bekenstein–Hawking 1/4 from null structure in d = 4, and the Sakharov (bottom-up) and Jacobson (top-down) routes meet at rk(E8) = 8 = dim T*M. Falsifiable signature: the logarithmic correction c_log = 4a = 31·dim(E8)/45 = 170.84 (PRED-087), where the universal vector-anomaly numerator 31 equals h∨+1 for E8 and only for E8 — an accidental identity flagged in the text in the spirit of the program's own null-model discipline. Discrimination against D8/A8/E6 runs through dim(G): factors 2.1–3.2× (31× vs. SU(3)). Every claim is classified (Derived / Conditional / Open); the identification of (E8)₁ as the horizon dual is stated as conditional on ER=EPR / Ryu–Takayanagi throughout.

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-08-25
DOI
https://doi.org/10.5281/zenodo.22100430
Primary Topic
Black Holes and Theoretical Physics
Type
preprint
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preprint

Black Hole Microstates as (E8)₁ CFT States — Closing the Sakharov–Jacobson Circle via the E8 Root Lattice

E.U.O.
Zenodo (CERN European Organization for Nuclear Research)
Black Holes and Theoretical Physics
preprint

Black Hole Microstates as (E8)₁ CFT States — Closing the Sakharov–Jacobson Circle via the E8 Root Lattice

E.U.O.
preprint en

Abstract

We identify the microstates of a Schwarzschild horizon as states of the chiral CFT (E8)₁ living on the horizon, counted by the Cardy formula with central charge c = 248/(1+30) = 8. This reframes the failure of naive lattice counting (ln 248 ≈ 5.51 per Planck cell, a factor ~22 too large) as a violation of the holographic principle — bulk counting gives S ~ V instead of S ~ A — and the 248 generators of E8 reappear correctly placed as the first excited level d(1) = 248 of the WZW character E4/η⁸ (1, 248, 4124, 34752, …). The algebraic identity 1/4 = (1+3)/(2·rk E8) connects the split-octonionic reduction O = 1+3+4 (which produces d = 4 with Lorentzian signature — a property D8 and A8 lack) with Wolfson's geometric derivation of the Bekenstein–Hawking 1/4 from null structure in d = 4, and the Sakharov (bottom-up) and Jacobson (top-down) routes meet at rk(E8) = 8 = dim T*M. Falsifiable signature: the logarithmic correction c_log = 4a = 31·dim(E8)/45 = 170.84 (PRED-087), where the universal vector-anomaly numerator 31 equals h∨+1 for E8 and only for E8 — an accidental identity flagged in the text in the spirit of the program's own null-model discipline. Discrimination against D8/A8/E6 runs through dim(G): factors 2.1–3.2× (31× vs. SU(3)). Every claim is classified (Derived / Conditional / Open); the identification of (E8)₁ as the horizon dual is stated as conditional on ER=EPR / Ryu–Takayanagi throughout.

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