PT-symmetric quantum mechanics began with a study of the Hamiltonian $H=p^2+ x^2(ix)^\epsilon$. The surprising feature of this non-Hermitian Hamiltonian is that its eigenvalues are discrete, real, and positive when $\epsilon>0$. In this talk we study the corresponding quantum-field-theoretic Hamiltonian $H=(\partial\phi)^2 +\phi^2(i\phi)^\epsilon$ in D-dimensional space-time, where $\phi$ is a...
Resurgence is a deep phenomenon found in a wide spectrum of mathematical and physical models. I will try to explain why this is the case and demonstrate its power, much of which lies still ahead.
I will talk on instanton effects in the Hofstadter problem.
In my talk I will describe application of resurgence to Chern-Simons topological quantum field theory on closed 3-manifolds.
An overview of recent developments in the applications of resurgence and transseries to string theory and 2d quantum gravity.
We address the puzzle of the light-like rolling in linear dilaton background relaxing to the tachyon vacuum. While we expect no perturbative fluctuations around the tachyon vacuum, and yet the tachyon relaxes to the vacuum, the resolution of this paradox comes in the form of an asymptotic series.
In the setting of the Painlevé I equation, which can be viewed as describing the double scaling limit of 2d quantum gravity, I describe techniques which can lead to a full understanding of the physics and mathematics encoded in resurgent asymptotic (trans)series.