Related papers: A Crossing-Symmetric OPE Inversion Formula
We study heavy-light four-point function by employing Lorentzian inversion formula, where the conformal dimension of heavy operator is as large as central charge $C_T\rightarrow\infty$. We implement the Lorentzian inversion formula back and…
In this note, we derive a Mellin space version of the Lorentzian inversion formula for CFTs by explicitly integrating over the cross-ratios in $d=2$ and $d=4$ spacetime dimensions. We use the simplicity of the Mellin representation of…
In this note, we present an alternative representation of the conformal block with external scalars in general spacetime dimensions in terms of a finite summation over Appell fourth hypergeometric function ${\bf{F}}_4$. We also construct…
We give a new perspective on the Lorentzian OPE inversion formula of arXiv:1703.00278, building on arXiv:2302.06469. We introduce an ``auxiliary'' fourpoint function that can be related to the traditionally defined ones via a Radon…
We set up the conventional conformal bootstrap equations in Mellin space and analyse the anomalous dimensions and OPE coefficients of large spin double trace operators. By decomposing the equations in terms of continuous Hahn polynomials,…
Motivated by AdS/CFT, we address the following outstanding question in large $N$ conformal field theory: given the appearance of a single-trace operator in the ${\cal O}\times{\cal O}$ OPE of a scalar primary ${\cal O}$, what is its total…
We elaborate on some general aspects of the crossing symmetric approach of Polyakov to the conformal bootstrap, as recently formulated in Mellin space. This approach uses, as building blocks, Witten diagrams in AdS. We show the necessity…
In the study of conformal field theories, conformal blocks in the lightcone limit are fundamental to the analytic conformal bootstrap method. Here we consider the lightcone limit of 4-point functions of generic scalar primaries. Based on…
We study the spectrum and OPE coefficients of the three-dimensional critical O(2) model, using four-point functions of the leading scalars with charges 0, 1, and 2 ($s$, $\phi$, and $t$). We obtain numerical predictions for low-twist OPE…
We study tools of the conformal bootstrap in simplifying limits, primarily a limit of large operator dimensions and small cross-ratios corresponding to non-relativistic physics in AdS. We show that T-channel conformal blocks give the…
Three-dimensional Chern-Simons vector models display an approximate higher spin symmetry in the large $N$ limit. Their single-trace operators consist of a tower of weakly broken currents, as well as a scalar $\sigma$ of approximate twist…
In this note we consider the problem of extracting the corrections to CFT data induced by the exchange of a primary operator and its descendents in the crossed channel. We show how those corrections which are analytic in spin can be…
One of the most striking successes of the lightcone bootstrap has been the perturbative computation of the anomalous dimensions and OPE coefficients of double-twist operators with large spin. It is expected that similar results for…
We describe how to implement the conformal bootstrap program in the context of the embedding space OPE formalism introduced in previous work. To take maximal advantage of the known properties of the scalar conformal blocks for…
We describe in more detail our approach to the conformal bootstrap which uses the Mellin representation of $CFT_d$ four point functions and expands them in terms of crossing symmetric combinations of $AdS_{d+1}$ Witten exchange functions.…
We investigate the heavy-light four-point function up to double-stress-tensor, supplementing 1910.06357. By using the OPE coefficients of lowest-twist double-stress-tensor in the literature, we find the Regge behavior for lowest-twist…
We solve crossing equations analytically in the deep Euclidean regime. Large scaling dimension $\Delta$ tails of the weighted spectral density of primary operators of given spin in one channel are matched to the Euclidean OPE data in the…
Starting from the Lorentzian inversion formula, we derive a dispersion relation which computes a four-point function in 1d CFTs as an integral over its double discontinuity. The crossing symmetric kernel of the integral is given explicitly…
We describe examples of drastic truncations of conformal bootstrap equations encoding much more information than that obtained by a direct numerical approach. A three-term truncation of the four point function of a free scalar in any space…
We compute anomalous dimensions of higher spin operators in Conformal Field Theory at arbitrary space-time dimension by using the OPE inversion formula of \cite{Caron-Huot:2017vep}, both from the position space representation as well as…