# 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…

## 11 Citations

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…

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

- Physics, Mathematics
- 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…

Correlation functions and quantum measures of descendant states

- Physics
- 2021

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…

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…

Critical non-Abelian vortices and holography for little string theory

- PhysicsPhysical Review D
- 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.…

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…

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

- Medicine, 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].

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…

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…

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,…

## References

SHOWING 1-10 OF 72 REFERENCES

Two-dimensional O(n) models and logarithmic CFTs

- PhysicsJournal of High Energy Physics
- 2020

Abstract
We study O(n)-symmetric two-dimensional conformal field theories (CFTs) for a continuous range of n below two. These CFTs describe the fixed point behavior of self-avoiding loops. There is…

The analytic bootstrap equations of non-diagonal two-dimensional CFT

- Physics
- 2017

A bstractUnder the assumption that degenerate fields exist, diagonal CFTs such as Liouville theory can be solved analytically using the conformal bootstrap method. Here we generalize this approach to…

Three-Point Functions in c≤1 Liouville Theory and Conformal Loop Ensembles.

- Physics, MedicinePhysical review letters
- 2016

It is shown in this Letter that this Liouville conformal field theory can be interpreted in terms of microscopic loop models and in particular a family of geometrical operators are introduced, and it is shown that their operator algebra corresponds exactly to that of vertex operators V_{α[over ^]} in c≤1Liouville theory.

Logarithmic M(2,p) minimal models, their logarithmic couplings, and duality

- Physics
- 2008

Abstract A natural construction of the logarithmic extension of the M ( 2 , p ) (chiral) minimal models is presented, which generalises our previous model of percolation ( p = 3 ). Its key aspect is…

Loop Models and Boundary CFT

- Physics
- 2012

We present a range of exact techniques within two-dimensional conformal field theory (CFT), using the Q-state Potts and the O(n) models as exploratory tools. Both are equivalent to models of oriented…

Puzzle of bulk conformal field theories at central charge c = 0.

- Physics, MathematicsPhysical review letters
- 2012

It is shown that, while the chiral stress tensor has indeed a single logarithmic partner in the Chiral sector of the theory, the value of b is not the expected one; instead, b=-5 for both theories.

Logarithmic conformal field theory: beyond an introduction

- Mathematics, Physics
- 2013

This article aims to review a selection of central topics and examples in logarithmic conformal field theory. It begins with the remarkable observation of Cardy that the horizontal crossing…

Non-chiral logarithmic couplings for the Virasoro algebra

- Mathematics, Physics
- 2012

This paper initiates the study of what we call non-chiral staggered Virasoro modules, indecomposable modules on which two copies of the Virasoro algebra act with the zero-modes L0 and acting…

Null vectors in logarithmic conformal field theory

- Physics, Mathematics
- 2000

The representation theory of the Virasoro algebra in the case of a logarithmic conformal eld theoryis considered. Here, indecomposablerepresentationshaveto be takeninto account,which has many…

Walking, Weak first-order transitions, and Complex CFTs II. Two-dimensional Potts model at $Q>4$

- PhysicsSciPost Physics
- 2018

We study complex CFTs describing fixed points of the two-dimensional
QQ-state
Potts model with Q≻ 4Q>4.
Their existence is closely related to the weak first-order phase
transition and the "walking"…