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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.