Abstract
We discuss, in conformally invariant field theories such as QCD with massless fermions, a possible link between the perturbative signature of the conformal anomaly, in the form of anomaly poles of the 1-particle irreducible effective action, and its descrip- tion in terms of Wess-Zumino actions with a dilaton. The two descriptions are expected to capture the UV and IR behaviour of the conformal anomaly, in terms of fundamental and effective degrees of freedom respectively, with the dilaton effective state appearing in a nonlinear realization. As in the chiral case, conformal anomalies seem to be related to the appearance of these effective interactions in the 1PI action in all the gauge-invariant sectors of the Standard Model. We show that, as a consequence of the underlying anomalous symmetry, the infinite hierarchy of recurrence relations involving self-interactions of the dilaton is entirely determined only by the first four of them. This relation can be generalized to any even space-time dimension.
Highlights
Conformal anomalies play a significant role in theories which are classically scale invariant, such as QCD
If the spontaneous breaking of symmetries is associated with massless Goldstone modes of a theory, it is natural to associate to the anomalous breaking of the conformal symmetry a massless state, identified as the dilaton
If the anomaly pole is the signature of the pseudo-Goldstone boson of the broken conformal symmetry, we should look for an action which reproduces the same anomaly and is suitable for the description of this virtual exchange as a composite asymptotic field
Summary
Conformal anomalies play a significant role in theories which are classically scale invariant, such as QCD. This type of anomaly manifests as a non-vanishing trace of the vacuum expectation value (vev) of the energy momentum tensor in a metric (gμν) and gauge field (Aμ) background. If the spontaneous breaking of symmetries is associated with massless Goldstone modes of a theory, it is natural to associate to the anomalous breaking of the conformal symmetry a massless state, identified as the dilaton. Non-perturbative effects may be responsible for the generation of a mass for this state, as do radiative corrections in the form of a usual Coleman-Weinberg potential, by a perturbative resummation. The anomaly is expressed by the functional relation gμν T μν s
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