Sum rules and spectral density flow in QCD and in superconformal theories

TL;DR

This paper investigates how superconformal symmetry breaking manifests through anomaly poles and spectral density flow in $ ext{N}=1$ super Yang Mills theory, revealing the emergence of composite states from spectral flow and sum rules.

Contribution

It introduces a detailed analysis of spectral density flow in deformed $ ext{N}=1$ theories and links anomaly poles to composite axion/dilaton/dilatino multiplets.

Findings

Spectral densities flow with mass deformations, transforming cuts into poles.

Anomaly poles indicate the exchange of composite ADD multiplets.

Global anomalous currents predict the existence of composite interpolating fields.

Abstract

We discuss the signature of the anomalous breaking of the superconformal symmetry in $\mathcal{N}=1$ super Yang Mills theory and its manifestation in the form of anomaly poles. Moreover, we describe the massive deformations of the $\mathcal{N}=1$ theory and the spectral densities of the corresponding anomaly form factors. These are characterized by spectral densities which flow with the mass deformation and turn the continuum contributions from the two-particle cuts of the intermediate states into poles, with a single sum rule satisfied by each component. The poles can be interpreted as signaling the exchange of a composite axion/dilaton/dilatino (ADD) multiplet in the effective Lagrangian. We conclude that global anomalous currents characterized by a single flow in the perturbative picture always predict the existence of composite interpolating fields.