Bootstrapping 2D CFTs in the Semiclassical Limit

TL;DR

This paper investigates two-dimensional conformal field theories in the semiclassical limit, deriving universal formulas for structure constants and applying these to specific orbifold models to produce bounds and corrected entropy formulas.

Contribution

It introduces a universal formula for structure constants involving heavy primaries in 2D CFTs within the semiclassical limit, simplifying crossing equations and enabling new bounds.

Findings

Derived the Hellerman bound for $ ext{Z}_2$ twist fields.

Produced a logarithmically corrected Cardy formula for $h \,\geq\, c/12$.

Showed that four-point functions are dominated by specific intermediate primaries.

Abstract

We study two dimensional conformal field theories in the semiclassical limit. In this limit, the four-point function is dominated by intermediate primaries of particular weights along with their descendants, and the crossing equations simplify drastically. For a four-point function receiving sufficiently small contributions from the light primaries, the structure constants involving heavy primaries follow a universal formula. Applying our results to the four-point function of the $\mathbb Z_2$ twist field in the symmetric product orbifold, we produce the Hellerman bound and the logarithmically corrected Cardy formula that is valid for $h \geq c/12$.