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Mathematician Ramanujan's infinite series for 1/π have a physics origin in 2D logarithmic conformal field theories (LCFTs). This connection reveals new approximations for 1/π and simplifies LCFT calculations.

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Area of Science:

  • Theoretical Physics
  • Mathematical Physics
  • Condensed Matter Theory

Background:

  • In 1914, Srinivasa Ramanujan discovered 17 remarkable infinite series for the reciprocal of pi (1/π).
  • Logarithmic conformal field theories (LCFTs) appear in diverse physical systems, including the fractional quantum Hall effect, percolation, and polymer physics.

Purpose of the Study:

  • To uncover the physics origin of Ramanujan's 17 infinite series for 1/π.
  • To establish a connection between these series and 2D logarithmic conformal field theories (LCFTs).
  • To reinterpret Ramanujan's series using fundamental conformal field theory (CFT) data and develop new approximations for 1/π.

Main Methods:

  • Relating Ramanujan's infinite series to 2D logarithmic conformal field theories (LCFTs).
  • Reinterpreting the series in terms of CFT operator spectrum and OPE coefficients.
  • Developing novel bases for LCFT correlators using stringy/parametric crossing-symmetric dispersion relations.
  • Analyzing the effect of a specific differential operator on these new expansions.

Main Results:

  • A direct link between Ramanujan's 1/π series and the physics of 2D LCFTs was established.
  • New physics-inspired approximations for 1/π were derived.
  • A new family of bases for LCFT correlators was constructed, demonstrating significantly faster convergence than standard methods.
  • A differential operator was shown to dramatically enhance convergence in these new expansions, simplifying LCFT calculations.

Conclusions:

  • Ramanujan's series for 1/π originate from fundamental properties of 2D LCFTs.
  • The LCFT framework provides novel insights and computational tools for both mathematics and physics.
  • The observed simplification suggests a universal property within LCFTs, with potential holographic interpretations.