Nuclear Physics & RIKEN Theory Seminar
"Resurgence theory, ghost instantons and analytical continuation of path integrals"
Presented by Gokce Basar, Stony Brook
Friday, October 4, 2013, 2 pm
Small Seminar Room, Bldg. 510
Hosted by: Shu Lin
A general quantum mechanical or quantum field theoretical system in the path integral formulation has both real and complex saddles (instantons and ghost-instantons). Resurgent asymptotic analysis implies that both types of saddles contribute to physical observables, even if the complex saddles are not on the integration path i.e., the associated Stokes multipliers are zero. I show explicitly that instanton-anti-instanton and ghostâ€"anti-ghost saddles both affect the expansion around the perturbative vacuum via a self-dual model in which the analytic continuation of the partition function to negative values of coupling constant gives a pathological exponential growth, but a homotopically independent combination of integration cycles (Lefschetz thimbles) results in a sensible theory. These two choices of the integration cycles are tied with a quantum phase transition. The general set of ideas in this construction may provide new insights into non-perturbative QFT, string theory, quantum gravity, and the theory of quantum phase transitions.