Seiberg duality versus hidden local symmetry

TL;DR

This paper investigates the connection between Seiberg duality and hidden local symmetry in SQCD, deriving the magnetic theory via HLS, and exploring symmetry restoration, parameter interpolation, and extensions to other gauge groups.

Contribution

It provides a detailed derivation of the magnetic theory using HLS, linking Seiberg duality to symmetry restoration and extending the formalism to other gauge groups.

Findings

HLS formalism reproduces Seiberg duals for various groups.

Parameter 'a' interpolates between vector meson dominance and mesonic limits.

Symmetry restoring directions relate to R-symmetry and duality.

Abstract

It is widely believed that the emergent magnetic gauge symmetry of SQCD is analogous to a hidden local symmetry (HLS). We explore this idea in detail, deriving the entire (spontaneously broken) magnetic theory by applying the HLS formalism to spontaneously broken SU(N) SQCD. We deduce the K\"ahler potential in the HLS description, and show that gauge and flavour symmetry are smoothly restored along certain scaling directions in moduli space. We propose that it is these symmetry restoring directions, associated with the R-symmetry of the theory, that allow full Seiberg duality. Reconsidering the origin of the magnetic gauge bosons as the rho-mesons of the electric theory, colour-flavour locking allows a simple determination of the parameter "a". Its value continuously interpolates between a=2 on the baryonic branch of moduli space - corresponding to "vector meson dominance" - and a=1 on the mesonic branch. Both limiting values are consistent with previous results in the literature. The HLS formalism is further applied to SO and Sp groups, where the usual Seiberg duals are recovered, as well as adjoint SQCD. Finally we discuss some possible future applications, including (naturally) the unitarisation of composite W scattering, blended Higgs/technicolour models, real world QCD and non-supersymmetric dualities.