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...

Guica, Monica

The $J\bar T$ deformation, built from the components of the stress tensor and of a $U(1)$ current, is a universal irrelevant deformation of two-dimensional CFTs that preserves the left-moving conformal symmetry, while breaking locality on the right-moving side. Operators in the $J\bar T$-deformed CFT are naturally labeled by the left-moving positio...

Bena, Iosif Heidmann, Pierre Turton, David
Published in
Journal of High Energy Physics

AdS2 plays an extremely important role in black-hole physics. We construct several infinite families of supergravity solutions that are asymptotically AdS2 in the UV, and terminate in the IR with a cap that is singular in two dimensions but smooth in ten dimensions. These solutions break conformal invariance, and should correspond to supersymmetric...

Guica, Monica

It has been recently shown that the deformation of an arbitrary two-dimensional conformal field theory by the composite irrelevant operator T (T) over bar, built from the components of the stress tensor, is solvable; in particular, the finite-size spectrum of the deformed theory can be obtained from that of the original CFT through a universal form...

Bzowski, Adam Guica, Monica
Published in
Journal of High Energy Physics

Recently, a non-local yet possibly UV-complete quantum field theory has been constructed by deforming a two-dimensional CFT by the composite operator JT¯\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddside...

Donnay, Laura Puhm, Andrea Strominger, Andrew
Published in
Journal of High Energy Physics

The four-dimensional S-matrix is reconsidered as a correlator on the celestial sphere at null infinity. Asymptotic particle states can be characterized by the point at which they enter or exit the celestial sphere as well as their SL(2, ℂ) Lorentz quantum numbers: namely their conformal scaling dimension and spin h±h¯\documentclass[12pt]{minimal} \...

Jacobsen, Jesper Lykke Saleur, Hubert
Published in
Journal of High Energy Physics

We revisit in this paper the problem of connectivity correlations in the Fortuin-Kasteleyn cluster representation of the two-dimensional Q-state Potts model conformal field theory. In a recent work [1], results for the four-point functions were obtained, based on the bootstrap approach, combined with simple conjectures for the spectra in the differ...

Rychkov, Slava Stergiou, Andreas

Fixed points of scalar field theories with quartic interactions in $d=4-\varepsilon$ dimensions are considered in full generality. For such theories it is known that there exists a scalar function $A$ of the couplings through which the leading-order beta-function can be expressed as a gradient. It is here proved that the fixed-point value of $A$ is...

Belavin, Vladimir Haraoka, Yoshishige Santachiara, Raoul
Published in
Communications in Mathematical Physics

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...