Scale and conformal invariance in field theory: a physical counterexample

Riva, V.; Cardy, John

doi:10.1016/j.physletb.2005.07.010

Cited by 86 publications

(115 citation statements)

References 2 publications

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“…This was first noted by Coleman and Jackiw [22] in d = 4. It was studied in detail in d = 2 by Riva and Cardy (RC) [23], who also observed that it has a Euclidean interpretation as the theory of elasticity.…”

Section: Examplesmentioning

confidence: 99%

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

Luty

Polchinski

Rattazzi

2013

J. High Energ. Phys.

212

399

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We 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.

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Section: Examplesmentioning

confidence: 99%

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

Luty

Polchinski

Rattazzi

2013

J. High Energ. Phys.

212

399

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show abstract

“…The functional derivative of the virial current with respect to φ 0 is an operator of dimension three and hence we can write its most general form 16) for some constants a k , b, c, where j µ k is a set of currents of dimension 3 including possibly V µ . This leads tô…”

Section: T T Omentioning

confidence: 99%

Comments on scale and conformal invariance

Bzowski

Skenderis

2014

J. High Energ. Phys.

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There has been recent interest in the question of whether four dimensional scale invariant unitary quantum field theories are actually conformally invariant. In this note we present a complete analysis of possible scale anomalies in correlation functions of the trace of the stress-energy tensor in such theories. We find that 2-, 3-and 4-point functions have a non-trivial anomaly while connected higher point functions are non-anomalous. We pay special attention to semi-local contributions to correlators (terms with support on a set containing both coincident and separated points) and show that the anomalies in 3-and 4-point functions can be accounted for by such contributions. We discuss the implications of the our results for the question of scale versus conformal invariance.

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“…See e.g. [37][38] how the generic choices of the kinetic term break conformal invariance while preserving the scale invariance.…”

Section: Introductionmentioning

confidence: 99%

Holographic renormalization of foliation preserving gravity and trace anomaly

Nakayama¹

2012

Gen Relativ Gravit

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From the holographic renormalization group viewpoint, while the scale transformation plays a primary role in holographic dualities by providing the extra dimension, the special conformal transformation seems to only play a secondary role.We, however, claim that the space-time diffeomorphism is crucially related to the latter. For its demonstration, we study the holographic renormalization group flow of a foliation preserving diffeomorphic theory of gravity (a.k.a. space-time flipped Horava gravity). We find that the dual field theory, if any, is only scale invariant but not conformal invariant. In particular, we show that the holographic trace anomaly in four dimension predicts the Ricci scalar squared term that would be incompatible with the Wess-Zumino consistency condition if it were conformal. This illustrates how the foliation preserving diffeomorphic theory of gravity could be in conflict with a theorem of the dual unitary quantum field theory.

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Scale and conformal invariance in field theory: a physical counterexample

Abstract: In this note, we illustrate how the two-dimensional theory of elasticity provides a physical example of field theory displaying scale but not conformal invariance.

Cited by 86 publications

References 2 publications

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

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

Comments on scale and conformal invariance

Holographic renormalization of foliation preserving gravity and trace anomaly

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