  We show that 3d SU(2) lattice Yang--Mills theory can be cast in the form of
an exact string representation. The derivation starts from the exact dual (or
spin foam) representation of the lattice gauge theory. We prove that every dual
configuration (or spin foam) can be equivalently described as a self--avoiding
worldsheet of strings on a framing of the lattice. Using this correspondence,
we translate the partition function into a sum over closed worldsheets that are
weighted with explicit amplitudes. The expectation value of two Polyakov loops
with spin j becomes a sum over worldsheets that are bounded by 2j strings along
a framing of the loops.

High Energy Physics - Theory;High Energy Physics - Lattice