For expansions in one-dimensional conformal blocks, we provide a rigorous link between the asymptotics of the spectral density of exchanged primaries and the leading singularity in the crossed channel. Our result has a direct application to systems of SL(2, ℝ)-invariant correlators (also known as 1d CFTs). It also puts on solid ground a part of the lightcone bootstrap analysis of...
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 popular functionals involving...
Department 6 Slava Rychkov 7 Boston , MA 02215 , U.S.A 8 24 rue Lhomond , 75231 Paris Cedex 05 , France 9 PSL Research University , CNRS, Sorbonne Universit ́es, UPMC Univ. Paris 06 Hamiltonian Truncation
We derive a dispersion relation for the S parameter in the SO(5)/SO(4) Minimal Composite Higgs model. This generalizes the Peskin-Takeuchi formula to the case when a light Higgs boson is present in the spectrum. Our result combines an IR effect due to the reduction in the Higgs boson couplings with a UV contribution from the strong sector. It also includes a finite matching term...
We revisit the electroweak precision tests for Higgsless models of strong EWSB. We use the Vector Meson Dominance approach and express S and T via couplings characterizing vector and axial spin-1 resonances of the strong sector. These couplings are constrained by the elastic unitarity and by requiring a good UV behavior of various form- factors. We pay particular attention to the...
Conformal blocks in any number of dimensions depend on two variables z, \( \overline{z} \). Here we study their restrictions to the special “diagonal” kinematics \( z=\overline{z} \), previously found useful as a starting point for the conformal bootstrap analysis. We show that conformal blocks on the diagonal satisfy ordinary differential equations, third-order for spin zero and...
We derive a general sum rule relating the Higgs coupling to W and Z bosons to the total cross section of longitudinal gauge boson scattering in I = 0, 1, 2 isospin channels. The Higgs coupling larger than in the Standard Model implies enhancement of the I = 2 cross section. Such an enhancement could arise if the Higgs sector is extended by an isospin-2 scalar multiplet including...
We develop the embedding formalism for conformal field theories, aimed at doing computations with symmetric traceless operators of arbitrary spin. We use an indexfree notation where tensors are encoded by polynomials in auxiliary polarization vectors. The efficiency of the formalism is demonstrated by computing the tensor structures allowed in n-point conformal correlation...
For conformal field theories in arbitrary dimensions, we introduce a method to derive the conformal blocks corresponding to the exchange of a traceless symmetric tensor appearing in four point functions of operators with spin. Using the embedding space formalism, we show that one can express all such conformal blocks in terms of simple differential operators acting on the basic...
