Resurgence theory, ghost-instantons, and analytic continuation of path integrals
By G. Basar, G. Dunne, M. Unsal. Journal of High Energy Physics, 2013
150 citations recorded by the source corpus.
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. We show explicitly that instanton-anti-instanton and ghost-anti-ghost saddles both affect the expansion around the perturbative vacuum. We study 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 our construction may provide new insights into non-perturbative QFT, string theory, quantum gravity, and the theory of quantum phase transitions.
Subfields: Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/65b37848bbe74962e64ef3f979f9ff6f7f157049
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In Atomic and Molecular Physics, and Optics
In Nuclear and High Energy Physics
Citations in the corpus
- An introduction to resurgence, trans-series and alien calculus (2014, background): “ condition. It is possible to obtain theories where one has multiple instantonic congurations with dierent actions S a;S b;:::[41], and even complex valued action for the so called ghost-instantons [42] or more generically non-topological saddle points [29]. For a more complete treatment of { 24 { m”