Low-energy effective theories of quantum spin and quantum link models - art. no. 085007

Quantum spin and quantum link models provide an unconventional regularizati on of field theory in which classical fields arise via dimensional reductio n of discrete variables. This D-theory regularization leads to the same con tinuum theories as the conventional approach. We show this by deriving the low-energy effective Lagrangians of D-theory models using coherent state pa th integral techniques. We illustrate our method for the (2+1)D Heisenbeg q uantum spin model which is the D-theory regularization of the 2D O(3) model . Similarly, we prove that in the continuum Limit a (2+1)D quantum spin mod el with SU(N)(L)xSU(N)(R) xU(1)(L=R) symmetry is equivalent to the 2D princ ipal chiral model. Finally, we show that (4+1)D SU(N) quantum link models r educe to ordinary 4D Yang-Mills theory.