Anomaly Poles as Common Signatures of Chiral and Conformal Anomalies

TL;DR

The paper demonstrates that anomaly poles are a general feature of both chiral and conformal anomalies, appearing in the AVV/AAA and TJJ correlators under broad kinematic conditions. Through explicit perturbative calculations and a longitudinal/transverse decomposition, it shows that these poles control UV behavior while decoupling in the IR, leading to UV unitarity challenges in anomalous theories. The conformal case is treated analogously via the Riegert nonlocal action, confirming a massless pole accounts for the trace anomaly in general kinematics. The results unify the understanding of anomalous effective actions and illuminate their implications for gauge and gravitational interactions at high energies.

Abstract

One feature of the chiral anomaly, analyzed in a perturbative framework, is the appearance of massless poles which account for it. They are identified by a spectral analysis of the anomaly graph and are usually interpreted as being of an infrared origin. Recent investigations show that their presence is not just confined in the infrared, but that they appear in the effective action under the most general kinematical conditions, even if they decouple in the infrared. Further studies reveal that they are responsible for the non-unitary behaviour of these theories in the ultraviolet (UV) region. We extend this analysis to the case of the conformal anomaly, showing that the effective action describing the interaction of gauge fields with gravity is characterized by anomaly poles that give the entire anomaly and are decoupled in the infrared (IR), in complete analogy with the chiral case. This complements a related analysis by Giannotti and Mottola on the trace anomaly in gravity, in which an anomaly pole has been identified in the corresponding correlator using dispersion theory in the IR. Our extension is based on an exact computation of the off-shell correlation function involving an energy-momentum tensor and two vector currents (the gauge-gauge-graviton vertex) which is responsible for the appearance of the anomaly.

Figures (4)

• Figure 1: Triangle diagram and momentum conventions for an AVV correlator.
• Figure 2: The amplitude $\Delta^{\lambda\mu\nu}(k_1,k_2)$ shown in $a)$ for the kinematical configuration $k_1^2=k_2^2=0$ reduces to the polar form depicted in $b)$ and given by Eq. (\ref{['IRpole']}).
• Figure 3: A "two-triangles" anomaly amplitude in the $s$-channel which is pole-dominated. In this case we have assumed $A$ to be a non-anomalous gauge boson while $B$ is anomalous.
• Figure 4: The complete one-loop vertex $\Gamma^{\mu \nu \alpha\beta}$ in $a)$ obtained as the sum of two 1PI contributions in $b)$ and $c)$ and of their Bose symmetric diagrams.