Line of critical points in 2+1 dimensions: quantum critical loop gases and non-Abelian gauge theory.
In this Letter, we (1) construct a one-parameter family of lattice models of interacting spins; (2) obtain their exact ground states; (3) derive a statistical-mechanical analogy which relates their ground states to O(n) loop gases; (4) show that the models are critical for d</=sqrt[2], where d parametrizes the models; (5) note that, for the special values d=2cos([pi/(k+2)], they are related to doubled level-k SU(2) Chern-Simons theory; (6) conjecture that they are in the universality class of a nonrelativistic SU(2) gauge theory; and (7) show that its one-loop beta function vanishes for all values of the coupling constant, implying that it is also on a critical line.
Freedman
Michael
M
Microsoft Research, One Microsoft Way, Redmond, Washington 98052, USA.
Nayak
Chetan
C
Shtengel
Kirill
K