Ikhlef, Yacine Shimada, Hirohiko

In generic conformal field theories with $W_3$ symmetry, we identify a primary field $\sigma$ with rational Kac indices, which produces the full $\mathbb{Z}_3$ charged and neutral sectors by the fusion processes $\sigma \times \sigma$ and $\sigma \times \sigma^*$, respectively. In this sense, this field generalises the $\mathbb{Z}_3$ fundamental sp...

Bautista, Teresa Dabholkar, Atish Erbin, Harold

A proper definition of the path integral of quantum gravity has been a long-standing puzzle because the Weyl factor of the Euclidean metric has a wrong-sign kinetic term. We propose a definition of two-dimensional Liouville quantum gravity with cosmological constant using conformal bootstrap for the timelike Liouville theory coupled to supercritica...

Paulos, Miguel F. Zan, Bernardo

We apply recently constructed functional bases to the numerical conformal bootstrap for 1D CFTs. We argue and show that numerical results in this basis converge much faster than the traditional derivative basis. In particular, truncations of the crossing equation with even a handful of components can lead to extremely accurate results, in oppositio...

Poland, David Rychkov, Slava Vichi, Alessandro

Conformal field theories have been long known to describe the fascinating universal physics of scale invariant critical points. They describe continuous phase transitions in fluids, magnets, and numerous other materials, while at the same time sit at the heart of our modern understanding of quantum field theory. For decades it has been a dream to s...

Mazáč, Dalimil Paulos, Miguel F.
Published in
Journal of High Energy Physics

We clarify the relationships between different approaches to the conformal bootstrap. A central role is played by the so-called extremal functionals. They are linear functionals acting on the crossing equation which are directly responsible for the optimal bounds of the numerical bootstrap. We explain in detail that the extremal functionals probe t...

Mazáč, Dalimil Paulos, Miguel F.
Published in
Journal of High Energy Physics

We study a general class of functionals providing an analytic handle on the conformal bootstrap equations in one dimension. We explicitly identify the extremal functionals, corresponding to theories saturating conformal bootstrap bounds, in two regimes. The first corresponds to functionals that annihilate the generalized free fermion spectrum. In t...

Dupic, Thomas Estienne, Benoît Ikhlef, Yacine

We consider the two-dimensional $\mathfrak{sl}_n$ quantum Toda field theory with an imaginary background charge. This conformal field theory has a higher spin symmetry ($W_n$ algebra), a central charge $c \leq n-1$ and a continuous spectrum. Using the conformal bootstrap, we compute structure constants involving two arbitrary scalar fields and a se...

Qiao, Jiaxin Rychkov, Slava
Published in
Journal of High Energy Physics

The modern conformal bootstrap program often employs the method of linear functionals to derive the numerical or analytical bounds on the CFT data. These functionals must have a crucial “swapping” property, allowing to swap infinite summation with the action of the functional in the conformal bootstrap sum rule. Swapping is easy to justify for the ...

Rose, Félix Dupuis, Nicolas

We compute the zero-temperature conductivity in the two-dimensional quantum O(N) model using a nonperturbative functional renormalization-group approach. At the quantum critical point we find a universal conductivity σ*/σQ (with σQ=q2/h the quantum of conductance and q the charge) in reasonable quantitative agreement with quantum Monte Carlo simula...

Rychkov, Slava Simmons-Duffin, David Zan, Bernardo

We discuss the 4pt function of the critical 3d Ising model, extracted fromrecent conformal bootstrap results. We focus on the non-gaussianity Q - theratio of the 4pt function to its gaussian part given by three Wickcontractions. This ratio reveals significant non-gaussianity of the criticalfluctuations. The bootstrap results are consistent with a r...