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Article Dans Une Revue Journal of High Energy Physics Année : 2019

The analytic functional bootstrap. Part I: 1D CFTs and 2D S-matrices

Dalimil Mazáč
  • Fonction : Auteur

Résumé

We study a general class of functionals providing an analytic handle on the conformal bootstrap equations in one dimension. We explicitly identify the extremal functionals, corresponding to theories saturating conformal bootstrap bounds, in two regimes. The first corresponds to functionals that annihilate the generalized free fermion spectrum. In this case, we analytically find both OPE and gap maximization functionals proving the extremality of the generalized free fermion solution to crossing. Secondly, we consider a scaling limit where all conformal dimensions become large, equivalent to the large $AdS$ radius limit of gapped theories in $AdS_2$. In this regime we demonstrate analytically that optimal bounds on OPE coefficients lead to extremal solutions to crossing arising from integrable field theories placed in large $AdS_2$. In the process, we uncover a close connection between asymptotic extremal functionals and S-matrices of integrable field theories in flat space and explain how 2D S-matrix bootstrap results can be derived from the 1D conformal bootstrap equations. These points illustrate that our formalism is capable of capturing non-trivial solutions of CFT crossing.

Dates et versions

hal-02410955 , version 1 (14-12-2019)

Identifiants

Citer

Dalimil Mazáč, Miguel Fernandes Paulos. The analytic functional bootstrap. Part I: 1D CFTs and 2D S-matrices. Journal of High Energy Physics, 2019, 2019 (2), ⟨10.1007/JHEP02(2019)162⟩. ⟨hal-02410955⟩
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