Erlangen 2026 – wissenschaftliches Programm
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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik
MP 3: Quantum Field Theory I: Axiomatic, Probabilistic, Algebraic, Conformal
MP 3.5: Vortrag
Dienstag, 17. März 2026, 18:00–18:15, KH 02.013
Operator statistics from a simple approximate CFT — Alexander Altland1, Julian Sonner2, and •Konstantin Weisenberger1 — 1Institute for Theoretical Physics, University of Cologne, 50937 Cologne, Germany — 2Départment de Physique Théorique, Université de Genève, CH-1211 Genève 4, Switzerland
Recently, in the context of the AdS3/CFT2 correspondence, the notion of ensembles of 2d quantum field theories specified by distributions of OPE-coefficients and conformal dimensions {Cijk, hi, hi} has been introduced (Belin et al, JHEP09(2024)163). These ensembles, dubbed ‘approximate CFTs’ (aCFTs), are expected to be conformally invariant on average while also exhibiting signatures of quantum chaos. We give the first explicit construction of such an ensemble: Nc colors of Dirac fermions in the presence of quenched gauge-field disorder. For Nc=1, we present prescriptions for the calculation of moments of OPE coefficients and conformal dimensions, and use them to reconstruct all associated probability distributions of the theory. For Nc > 1, we apply the same methods to find the variance of OPE coefficients of bilinear fields. Finally, we also demonstrate the emergence of random matrix statistics upon perturbing the system by a mass operator.
Keywords: conformal field theory; disordered systems; quantum chaos