Bootstrapping 2D CFTs in the Semiclassical Limit

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 $h\ge c/12$.

32 pages, 7 figures. v2, v3: references added, minor clarifications

References in corpus (2)

• Universal Spectrum of 2d Conformal Field Theory in the Large c Limit
• Semiclassical Virasoro Blocks from AdS${}_3$ Gravity

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