Messengers from Imaginary Time: Instantons and the Complex Universe

The universe we observe is real — but the path integral that governs it runs over complex field configurations. Perturbation theory, mostly the default tool of quantum field theory, is blind to this complexity. Instantons are the exact classical solutions that see it: by minimizing the Euclidean action within each topological sector, they dominate the path integral between distinct vacua and act as messengers from imaginary time, t → −iτ, carrying news from the complex domain into observable, real-world physics.

This talk traces instantons from their simplest incarnation — a particle tunneling through a double-well potential — to their consequences at the heart of QCD: the structure of the θ-vacuum, the resolution of the U(1)_A problem, the strong CP problem and its axion solution, sphaleron-driven baryon number violation, and the instanton liquid model of chiral symmetry breaking. Along the way we encounter some of the deepest mathematics in modern physics: topology, self-duality, the Atiyah–Singer index theorem, and the emerging theory of resurgence, which reveals that perturbative and non-perturbative physics are not separate worlds but two sides of the same expansion — a fact made precise by resurgence, where the factorial divergence of the perturbative series is itself a fingerprint of the instanton sector.The second half of the talk turns to experiment. Can these messengers actually be detected? We review searches in deep inelastic scattering at HERA, the status of searches at the LHC, and the prospects for a first direct observation at the Electron-Ion Collider. No confirmed signal yet — but the next decade may change that..

The talk is self-contained and aims to be accessible to a broad audience, from bachelor students encountering path integrals for the first time to researchers working at the frontier of non-perturbative QCD.