Two-dimensional Born-Infeld gauge theory: spectrum, string picture and large-N phase transition

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.