The a-theorem and the asymptotics of 4D quantum field theory

By M. Luty, J. Polchinski, R. Rattazzi. 2012

271 citations recorded by the source corpus.

A bstractWe study the possible IR and UV asymptotics of 4D Lorentz invariant unitary quantum field theory. Our main tool is a generalization of the Komargodski-Schwimmer proof for the a-theorem. We use this to rule out a large class of renormalization group flows that do not asymptote to conformal field theories in the UV and IR. We show that the only possible UV and IR asymptotics described by perturbation theory have a vanishing trace of the stress-energy tensor, and are therefore conformal. Our arguments hold even for theories with gravitational anomalies. We also give a non-perturbative argument that excludes theories with scale but not conformal invariance. This argument holds for theories in which the stress-energy tensor is sufficiently nontrivial in a technical sense that we make precise.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/16f255a997658e2fb91485b45f1ff7a35a17faf9

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Astronomy and Astrophysics

In Nuclear and High Energy Physics

Citations in the corpus

Mutual information and the F-theorem (2015, background): “a-theorem in four dimensions [3, 4] — see also [5].”
EPFL Lectures on Conformal Field Theory in D ≥ 3 Dimensions (2016, background): “For recent work on scale vs conformal invariance see Luty, Polchinski and Rattazzi [11], Dymarsky, Komargodski, Schwimmer and Theisen [12], and the review by Nakayama [13].”
Deformations of superconformal theories (2016, background): “[0] (0;0) 1 Q // [1] (1;1) 3/2 Q // [2] (2;0) 2 ⊕ [2] (0;2) 2 ⊕ [0] (0;0) 2 Q // [3] (1;1) 5/2 Q // [4] (0;0) 3 (1.”
On the CFT operator spectrum at large global charge (2015, methodology): “The analysis of the Wess-Zumino term for anomalous Weyl symmetry has been carried out in [28] (see their eq.”
Convexity and liberation at large spin (2012, background): “The feasibility of this scenario has been discussed recently, for example, in [2-8].”
Conformal invariance in the long-range Ising model (2015, background): “” 30 See [48] for a review and in particular [49–51] for recent nontrivial progress in 4d.”
On renormalization group flows and the a-theorem in 6d (2012, background): “It is argued in [11] and [12] that these limits are controlled by operator deformations of the IR and UV CFT’s.”
Solid Inflation (2012, background): “In the spacetime symmetry case, there are fundamental reasons why that happens [12, 13].”