  We analyze U(N) Born-Infeld gauge theory in two spacetime dimensions. We
derive the exact energy spectrum on the circle and show that it reduces to N
relativistic fermions on a dual space. This contrasts to the Yang-Mills case
that reduces to nonrelativistic fermions. The theory admits a string theory
interpretation, analogous to the one for ordinary Yang-Mills, but with higher
order string interactions. We also demonstrate that the partition function on
the sphere exhibits a large-N phase transition in the area and calculate the
critical area. The limit in which the dimensionless coupling of the theory goes
to zero corresponds to massless fermions, admits a perturbatively exact free
string interpretation and exhibits no phase transition.
