title: Complex Path Integrals and Saddles in Two-Dimensional Gauge Theory.
abstract: We study numerically the saddle point structure of two-dimensional lattice gauge theory, represented by the Gross-Witten-Wadia unitary matrix model. The saddle points are, in general, complex valued, even though the original integration variables and action are real. We confirm the trans-series and instanton gas structure in the weak-coupling phase, and we identify a new complex-saddle interpretation of nonperturbative effects in the strong-coupling phase. In both phases, eigenvalue tunneling refers to eigenvalues moving off the real interval, into the complex plane, and the weak-to-strong coupling phase transition is driven by saddle condensation.
authors.affiliation: Institute for Theoretical Physics, Regensburg University, D-93053 Regensburg, Germany.
authors.forename: P V
authors.initials: PV
authors.lastname: Buividovich
authors.affiliation: Department of Physics, University of Connecticut, Storrs, Connecticut 06269-3046, USA.
authors.forename: Gerald V
authors.initials: GV
authors.lastname: Dunne
authors.affiliation: Institute for Theoretical Physics, Regensburg University, D-93053 Regensburg, Germany.|Institute of Theoretical and Experimental Physics (ITEP), B. Cheremushkinskaya Street 25, 117218 Moscow, Russia.
authors.forename: S N
authors.initials: SN
authors.lastname: Valgushev