Geometrical four-point functions in the two-dimensional critical Q-state Potts model: the interchiral conformal bootstrap
Yifei He, Jesper Lykke Jacobsen, Hubert Saleur
Abstract
A bstract Based on the spectrum identified in our earlier work [1], we numerically solve the bootstrap to determine four-point correlation functions of the geometrical connectivities in the Q -state Potts model. Crucial in our approach is the existence of “interchiral conformal blocks”, which arise from the degeneracy of fields with conformal weight h r, 1 , with r ∈ ℕ * , and are related to the underlying presence of the “interchiral algebra” introduced in [2]. We also find evidence for the existence of “renormalized” recursions, replacing those that follow from the degeneracy of the field $$ {\Phi}_{12}^D $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>Φ</mml:mi> <mml:mn>12</mml:mn> <mml:mi>D</mml:mi> </mml:msubsup> </mml:math> in Liouville theory, and obtain the first few such recursions in closed form. This hints at the possibility of the full analytical determination of correlation functions in this model.