Aspects of the S transformation Bootstrap

Abstract

We review and systematize two (analytic) bootstrap techniques in two-dimensional conformal field theories using the S-modular transformation. The first one gives universal results in asymptotic regimes by relating extreme temperatures. Along with the presentation of known results, we use this technique to also derive asymptotic formulae for the Zamolodchikov recursion coefficients which match previous conjectures from numerics and from Regge asymptotic analysis. The second technique focuses on intermediate temperatures. We use it to sketch a methodology to derive a bound on off-diagonal squared OPE coefficients, as well as to improve existing bounds on the spectrum in case of non-negative diagonal OPE coefficients.

arXiv comment27+7 pages, 3 figures, v2 : improved the numerics for torus-one-point function bootstrap, corrected a missing factor in the torus-two-point function, conclusions unchanged, and new references added

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• Universal Dynamics of Heavy Operators in CFT${}_2$
• High Energy Modular Bootstrap, Global Symmetries and Defects
• Analytic Bootstrap in 2D Boundary Conformal Field Theory: Towards Braneworld Holography
• Universality in asymptotic bounds and its saturation in $2$D CFT
• Discreteness and Integrality in Conformal Field Theory
• Virasoro blocks and quasimodular forms