Renormalization group flows, the a-theorem and conformal bootstrap

Abstract

Every renormalization group flow in d spacetime dimensions can be equivalently described as spectral deformations of a generalized free CFT in (d − 1) spacetime dimensions. This can be achieved by studying the effective action of the Nambu-Goldstone boson of broken conformal symmetry in anti-de Sitter space and then taking the flat space limit. This approach is particularly useful in even spacetime dimension where the change in the Euler anomaly a UV − a IR can be related to anomalous dimensions of lowest twist multi-trace operators in the dual CFT. As an application, we provide a simple proof of the 4d a-theorem using the dual description. Furthermore, we reinterpret the statement of the a-theorem in 6d as a conformal bootstrap problem in 5d.

A generalized Nachtmann theorem in CFT

“…At the leading order in the lightcone limit, for real positive σ < 1 we obtaiñ Similarly, we can analytic continue the lightcone conformal block along the path shown in figure 2 to obtainG mixed (η, σ) Op . In particular, using appendix B of [40], at the leading order in the Lorentzian lightcone limit, for real positive σ < 1, we find (when ∆ p is not an integer)…”

“…Similarly, we can analytic continue the Dolan-Osborn block along the path shown in figure 2 to obtain G(η, σ)| Op . In particular, using appendix B of [40], at the leading order in the Lorentzian lightcone limit we find…”

2-Group global symmetries and anomalies in six-dimensional quantum field theories

“…The resulting number is negative, a vector = − 251 210 . As emphasized in [42] this result is puzzling but not a contradiction: since the free N = (1, 0) vector multiplet is not an SCFT, there is no immediate meaning to the a-anomaly (or any 25 See [52] for an attempt at a proof along the lines of [51], and [53] for an attempt via the conformal bootstrap. 26 Similar N = (1, 0) anomaly multiplet relations for the ci-anomalies were proposed in [57,58] and proved in [59].…”

Swampland conditions for higher derivative couplings from CFT

“…f ∆+L ∆ ∆+L ∆ − 1 2 log (η) . (D. 19) In the limit η → 0, we obtain from (D.17) (see appendix D of [93]):…”

“…where the derivatives are taken with respect to the bulk point {z, x}. 25 In the above expression, we have utilized the notations of [93] AdS…”