What question did this study set out to answer?

This work aims to present a complete proof for the Ramanujan discriminant modular form evaluation using the Chowla–Selberg formula.

March 15, 2026Open Access

BCT Appendix JH3: Ramanujan's Vacuum — Complete Proof via the Chowla–Selberg Formula

Key Points

This work aims to present a complete proof for the Ramanujan discriminant modular form evaluation using the Chowla–Selberg formula.
Evaluation of the BCT instanton action using the Chowla–Selberg formula.
Identification of the BCT Superfluid Lattice Model with critical bosonic string compactification.
Analysis of the Dedekind eta function at the CM point τ = i.
Established that S_D4 = π5/6.
Showed the relevance of the modular form in the context of the superfluid model.
Provided a complete proof linking theoretical constructs to physical realizations.

Abstract

Complete proof that the BCT instanton action SD4 = π5/6 is the evaluation of the Ramanujan discriminant modular form Δ (τ) = η (τ) 24 at the CM point τ = i, via the Chowla–Selberg formula for the Dedekind eta function. Establishes the identification of the BCT Superfluid Lattice Model as the physical realisation of the critical bosonic string compactified on the D4 root lattice. Companion technical appendix to Letter 37.

BCT Appendix JH3: Ramanujan's Vacuum — Complete Proof via the Chowla–Selberg Formula

Key Points

Abstract

Cite This Study