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arXiv · 1512.09021

Complex Saddles in Two-dimensional Gauge Theory

P. V. Buividovich·Gerald V. Dunne·S. N. Valgushev
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Abstract

We study numerically the saddle point structure of two-dimensional (2D) 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/instanton gas structure in the weak-coupling phase, and identify a new complex-saddle interpretation of non-perturbative 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.

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P. V. Buividovich, Gerald V. Dunne, S. N. Valgushev. 2016-04-06. Complex Saddles in Two-dimensional Gauge Theory. https://doi.org/10.1103/physrevlett.116.132001

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