What question did this study set out to answer?

The aim is to derive the density-dependent coupling κ(ρ) and understand its intrinsic nature related to the tachyon vacuum.

March 24, 2026Open Access

CCEGA Paper 17: The Hard Threshold as an Intrinsic Property of the Sen Tachyon Vacuum — Exact Derivation of κ(ρ)

Key Points

The aim is to derive the density-dependent coupling κ(ρ) and understand its intrinsic nature related to the tachyon vacuum.
Exact derivation of κ(ρ) using mathematical tools like SymPy.
Analysis of Lagrangian non-analyticity and its implications on tachyon tension.
Comparison with previous findings from Paper 16 to verify consistency.
The coupling κ(ρ) diverges at a critical density ρ_c.
The result indicates a second-order phase transition analog at ρ_c.
The hard threshold emerges naturally, not as an imposed feature.

Abstract

Derives exactly the density-dependent coupling κ (ρ) deferred in Paper 16. The result diverges at ρc and vanishes at infinity. Shows this divergence is intrinsic to L∝φ^1/2: the tachyon tension T (φ) =T₀φ^-1/2 diverges at the vacuum φ=0, making ρc a critical point analogous to a second-order phase transition. The hard threshold is not imposed — it emerges from the non-analytic structure of the Lagrangian. Verified with SymPy. All predictions of Paper 16 unchanged.

CCEGA Paper 17: The Hard Threshold as an Intrinsic Property of the Sen Tachyon Vacuum — Exact Derivation of κ(ρ)

Key Points

Abstract

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