出版社：SISSA, Scuola Internazionale Superiore di Studi Avanzati
摘要：We find a strong-to-weak coupling cross-over in D
2 1 SU
N
lattice gauge theories that
appears to become a third-order phase transition at N
¥, in a similar way to the Gross-Witten
transition in the D
1 1 SU
N
¥
lattice gauge theory. There is, in addition, a peak in the
specific heat at approximately the same coupling that increases with N, which is connected to
ZN monopoles (instantons), reminiscent of the first order bulk transition that occurs in D
3 1
for N
5. Our calculations are not precise enough to determine whether this peak is due to a
second-order phase transition at N
¥ or to a third-order phase transition with different critical
behaviour to that of the Gross-Witten transition. We investigate whether the trace of the Wilson
loop has a non-analyticity in the coupling at some critical area, but find no evidence for this.
However we do find that, just as one can prove occurs in D
1 1, the eigenvalue density of a
Wilson loop forms a gap at N
¥ at a critical value of its trace. We show that this gap formation
is in fact a corollary of a remarkable similarity between the eigenvalue spectra ofWilson loops in
D
1 1 and D
2 1 (and indeed D
3 1): for the same value of the trace, the eigenvalue
spectra are nearly identical. This holds for finite as well as infinite N; irrespective of the Wilson
loop size in lattice units; and for Polyakov as well as Wilson loops.
