New formulations for dual equivalent actions

TL;DR

This paper introduces new dual equivalent actions in two and three dimensions that incorporate chiral and helicity constraints, along with an interpolating action connecting these dualities and exploring their symmetry properties.

Contribution

It proposes novel dual equivalent actions with dynamic constraints and a new interpolating formulation, extending the understanding of dualities and symmetry in lower-dimensional theories.

Findings

New dual actions in D=2 and D=3 with dynamic constraints

A novel interpolating action connecting dual theories

Analysis of duality mechanisms in condensed phases

Abstract

New actions in D=2 and D=3 are proposed that are dual equivalent to known theories displaying well defined chirality and helicity, respectively, along with a new interpolating action that maps continuously through the original dualities. The new chiral action in D=2 is a second-order theory displaying the chiral constraint dynamically while in D=3 the helicity constraint is imposed a la Siegel. The resulting theories introduce new versions of the Hull noton to take care of the symmetry aspects of the original models. The new interpolating formulation is then re-examined as a condensed phase for the discussion of duality under the light of the dual mechanisms -- Julia-Toulouse and Higgs -- establishing new interpolating actions in the dilute phase, according to these mechanisms.