# 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={arXiv: High Energy Physics - Theory}, 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… Expand

#### 11 Citations

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

- Physics
- SciPost Physics
- 2021

We revisit the critical two-dimensional Ashkin–Teller model, i.e. the
\mathbb{Z}_2ℤ2
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c=1c=1.
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Fusion in the periodic Temperley-Lieb algebra and connectivity operators of loop models

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- 2021

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… Expand

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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 vacuum… Expand

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

- Physics, 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… Expand

Critical Non-Abelian Vortex and Holography for Little String Theory

- Physics
- 2021

It has been shown that non-Abelian vortex string supported in four dimensional (4D) N = 2 supersymmetric QCD (SQCD) with the U(2) gauge group and Nf = 4 quark flavors becomes a critical superstring.… Expand

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

- Physics, Mathematics
- 2021

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… Expand

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

- Medicine, Physics
- Physical 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]. Expand

On the CFT describing the spin clusters in 2d Potts model

- Physics, Mathematics
- 2021

We have considered clusters of like spin in the Q-Potts model. Using Monte Carlo simulations, we studied the S clusters on a toric Lh × Lv square lattice for values of Q ∈ [1, 4]. We continue the… Expand

Particles, conformal invariance and criticality in pure and disordered systems

- Physics, Mathematics
- 2020

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… Expand

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

- Physics, 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,… Expand

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