A Duality Web in 2+1 Dimensions and Condensed Matter Physics

Understand

Building on earlier work in the high energy and condensed matter communities, we present a web of dualities in $2+1$ dimensions that generalize the known particle/vortex duality.

• Some of the dualities relate theories of fermions to theories of bosons.
• Others relate different theories of fermions.
• For example, the long distance behavior of the $2+1$-dimensional analog of QED with a single Dirac fermion (a theory known as $U(1)_{1/2}$) is identified with the $O(2)$ Wilson-Fisher fixed point.