Topological symmetry, spin liquids and CFT duals of Polyakov model with massless fermions

Understand

We prove the absence of a mass gap and confinement in the Polyakov model with massless complex fermions in any representation of the gauge group.

• A $U(1)_{*}$ topological shift symmetry protects the masslessness of one dual photon.
• This symmetry emerges in the IR as a consequence of the Callias index theorem and abelian duality.
• For matter in the fundamental representation, the infrared limits of this class of theories interpolate between weakly and strongly coupled conformal field theory (CFT) depending on the number of flavors, and provide an infinite class of CFTs in $d=3$ dimensions.