The topological ground state degeneracy(g.s.d.) provides useful information for a topological field theory(TQFT), such as this post shows some example.
To count g.s.d., it seems to be equivalent to count the volume of the symplectic phase space. As I have heard, it is known that a gauge theory with a non-compact gauge group the g.s.d. is infinity: $$ \text{g.s.d.}=\infty $$ (specifically, my interest can be 2+1D Chern-Simons theory; or other cases).
Question 1: Are there some explicit ways to demonstrate this $ \text{g.s.d.}=\infty $?
Question 2: Does non-compact gauge group necessarily(only if)/sufficiently(if) leads to a non-unitary theory?
Many thanks.
