Dupic, Thomas Estienne, Benoît Ikhlef, Yacine

We consider the two-dimensional quantum Toda field theory with an imaginary background charge. This conformal field theory has a higher spin symmetry (W n algebra), a central charge and a continuous spectrum. Using the conformal bootstrap, we compute structure constants involving two arbitrary scalar fields and a semi-degenerate field of Wyllard ty...

Belavin, Vladimir Haraoka, Yoshishige Santachiara, Raoul

We investigate Fuchsian equations arising in the context of 2-dimensional conformal field theory (CFT) and we apply the Katz theory of Fucshian rigid systems to solve some of these equations. We show that the Katz theory provides a precise mathematical framework to answer the question whether the fusion rules of degenerate primary fields are enough...

Kaviraj, Apratim Paulos, Miguel F.

We introduce a new approach to the study of the crossing equation for CFTs in the presence of a boundary. We argue that there is a basis for this equation related to the generalized free field solution. The dual basis is a set of linear functionals which act on the crossing equation to give a set of sum rules on the boundary CFT data: the functiona...

Gorbenko, Victor Rychkov, Slava Zan, Bernardo

We study complex CFTs describing fixed points of the two-dimensional$Q$-state Potts model with $Q>4$. Their existence is closely related to theweak first-order phase transition and walking RG behavior present in the realPotts model at $Q>4$. The Potts model, apart from its own significance, servesas an ideal playground for testing this very general...

Lauria, Edoardo Meineri, Marco Trevisani, Emilio

We study the two-point function of local operators in the presence of a defect in a generic conformal field theory. We define two pairs of cross ratios, which are convenient in the analysis of the OPE in the bulk and defect channel respectively. The new coordinates have a simple geometric interpretation, which can be exploited to efficiently comput...

Gorbenko, Victor Rychkov, Slava Zan, Bernardo

We discuss walking behavior in gauge theories and weak first-order phase transitions in statistical physics. Despite appearing in very different systems (QCD below the conformal window, the Potts model, deconfined criticality) these two phenomena both imply approximate scale invariance in a range of energies and have the same RG interpretation: a f...

Bzowski, Adam Mcfadden, Paul Skenderis, Kostas

We present a complete momentum-space prescription for the renormalisation of tensorial correlators in conformal field theories. Our discussion covers all 3-point functions of stress tensors and conserved currents in arbitrary spacetime dimensions. In dimensions three and four, we give explicit results for the renormalised correlators, the anomalous...

Bzowski, Adam Mcfadden, Paul Skenderis, Kostas

We discuss the renormalisation of mixed 3-point functions involving tensorial and scalar operators in conformal field theories of general dimension. In previous work we analysed correlators of either purely scalar or purely tensorial operators, in each case finding new features and new complications: for scalar correlators, renormalisation leads to...

Fateev, V.A. Litvinov, A.V.

We introduce and study conformal field theories specified by W −algebras commuting with certain set of screening charges. These CFT’s possess perturbations which define integrable QFT’s. We establish that these QFT’s have local and non-local Integrals of Motion and admit the perturbation theory in the weak coupling region. We construct factorized s...

Dornic, Ivan

We recast the persistence probability for the spin located at the origin of a half-space arbitrarily $m$-magnetized Glauber-Ising chain as a Fredholm Pfaffian gap probability generating function with a sech-kernel. This is then spelled out as a tau-function for a certain Painlev\'e VI transcendent, the persistence exponent $\theta(m)/2$ emerging as...