# Logarithmic CFT at generic central charge: from Liouville theory to the $Q$-state Potts model

@article{Nivesvivat2020LogarithmicCA, title={Logarithmic CFT at generic central charge: from Liouville theory to the \$Q\$-state Potts model}, author={Rongvoram Nivesvivat and Sylvain Ribault}, journal={SciPost Physics}, year={2020} }

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…

## 17 Citations

### The action of the Virasoro algebra in the two-dimensional Potts and loop models at generic Q

- Mathematics
- 2020

The spectrum of conformal weights for the CFT describing the two-dimensional critical $Q$-state Potts model (or its close cousin, the dense loop model) has been known for more than 30 years. However,…

### Analytic conformal bootstrap and Virasoro primary fields in the Ashkin-Teller model

- PhysicsSciPost Physics
- 2021

We revisit the critical two-dimensional Ashkin–Teller model, i.e. the
\mathbb{Z}_2ℤ2
orbifold of the compactified free boson CFT at
c=1c=1.
We solve the model on the plane by computing its…

### Particles, conformal invariance and criticality in pure and disordered systems

- MathematicsThe European Physical Journal B
- 2021

The two-dimensional case occupies a special position in the theory of critical phenomena due to the exact results provided by lattice solutions and, directly in the continuum, by the…

### Fusion in the periodic Temperley-Lieb algebra and connectivity operators of loop models

- MathematicsSciPost Physics
- 2022

In two-dimensional loop models, the scaling properties of critical random curves are encoded in the correlators of connectivity operators. In the dense O(n) loop model, any such operator is naturally…

### Topological effects and conformal invariance in long-range correlated random surfaces

- Mathematics
- 2020

We consider discrete random fractal surfaces with negative Hurst exponent $H<0$. A random colouring of the lattice is provided by activating the sites at which the surface height is greater than a…

### Correlation functions and quantum measures of descendant states

- PhysicsJournal of High Energy Physics
- 2021

Abstract
We discuss a computer implementation of a recursive formula to calculate correlation functions of descendant states in two-dimensional CFT. This allows us to obtain any N-point function of…

### Level Set Percolation in the Two-Dimensional Gaussian Free Field.

- PhysicsPhysical review letters
- 2021

Using a loop-model mapping, it is shown that there is a nontrivial percolation transition and characterize the critical point, and the critical clusters are "logarithmic fractals," whose area scales with the linear size as A∼L^{2}/sqrt[lnL].

### A note on the identity module in $c=0$ CFTs

- Mathematics
- 2021

It has long been understood that non-trivial Conformal Field Theories (CFTs) with vanishing central charge (c = 0) are logarithmic. So far however, the structure of the identity module – the (left…

### Global symmetry and conformal bootstrap in the two-dimensional $O(n)$ model

- MathematicsSciPost Physics
- 2022

We define the two-dimensional O(n) conformal field theory as a theory that includes the critical dilute and dense O(n) models as special cases, and depends analytically on the central charge.
For…

### Diagonal fields in critical loop models

- Mathematics
- 2022

: In critical loop models, there exist diagonal ﬁelds with arbitrary conformal dimensions, whose 3 -point functions coincide with those of Liouville theory at c ≤ 1 . We study their N -point…

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- 2020

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Abstract
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