On the Equivalence of Dual Theories

TL;DR

This paper investigates the classical and quantum non-equivalence of two dual scalar field theories in 2D, highlighting differences in their S-matrices and counterterms, and suggesting anomalies may cause dual model non-equivalence.

Contribution

It demonstrates that dual scalar theories derived from the same model can be non-equivalent at both classical and quantum levels, challenging assumptions of duality.

Findings

Tree S-matrices of the models do not coincide

One model is single-charged, the other multi-charged

Models are non-equivalent at quantum level due to anomalies

Abstract

We discuss the equivalence of two dual scalar field theories in 2 dimensions. The models are derived though the elimination of different fields in the same Freedman--Townsend model. It is shown that tree $S$-matrices of these models do not coincide. The 2-loop counterterms are calculated. It turns out that while one of these models is single-charged, the other theory is multi-charged. Thus the dual models considered are non-equivalent on classical and quantum levels. It indicates the possibility of the anomaly leading to non-equivalence of dual models.