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Logarithmic CFT at generic central charge: from Liouville theory to the $Q$-state Potts model
by Rongvoram Nivesvivat, Sylvain Ribault
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Submission summary
| Ontological classification |
| Academic field: |
Physics |
| Specialties: |
- High-Energy Physics - Theory
- Mathematical Physics
|
| Approach: |
Theoretical |
Abstract
Using derivatives of primary fields (null or not) with respect to the conformal dimension, we build infinite families of non-trivial logarithmic representations of the conformal algebra at generic central charge, with Jordan blocks of dimension $2$ or $3$. Each representation comes with one free parameter, which takes fixed values under assumptions on the existence of degenerate fields. This parameter can be viewed as a simpler, normalization-independent redefinition of the logarithmic coupling. We compute the corresponding non-chiral conformal blocks, and show that they appear in limits of Liouville theory four-point functions. As an application, we describe the logarithmic structures of the critical two-dimensional $O(n)$ and $Q$-state Potts models at generic central charge. The validity of our description is demonstrated by semi-analytically bootstrapping four-point connectivities in the $Q$-state Potts model to arbitrary precision. Moreover, we provide numerical evidence for the Delfino--Viti conjecture for the three-point connectivity. Our results hold for generic values of $Q$ in the complex plane and beyond.
List of changes
added clarifications and references following reviewers' suggestions, in particular in Section 2.2
