Understanding Phase Transitions in Supersymmetric Quantum Electrodynamics With Resurgence Theory

In quantum field theory (or QFT), perturbation theory is a mathematical approximation used to describe a complex quantum system with a simpler one. However, this approach is not valid for strongly coupled systems or phase transitions, for which the perturbative expansions are not convergent.

A technique called “resurgence theory” could, however, allow us to understand non-perturbative effects from information concealed within a perturbative series. This approach has been used to describe a wide range of systems in quantum mechanics, hydrodynamics, and string theory. But so far, there has been little focus on describing systems with phase transitions.

Against this backdrop, physicists from Japan studied the resurgence structure of a three-dimensional supersymmetric quantum electrodynamics (or SQED) model with a second-order quantum phase transition to explore the relations between resurgence and phase transitions.

The team used two approaches in their study: one involved a “Lefschetz thimble analysis,” in which the path integral representations of physical observables were decomposed in terms of Lefschetz thimbles. The thimble decomposition, in turn, could either change discontinuously to give rise to “Stokes phenomena” or remain unchanged but switch dominant saddle points to give “anti-Stokes phenomena.” The other was “Borel resummation technique,” which could decode these phenomena from a purely perturbative expansion.

The team interpreted the second-order phase transition as a simultaneous Stokes and anti-Stokes phenomena and showed that the order of phase transition was governed by the number of saddles colliding and by their collision angle at the critical point. In addition, supersymmetry led to an infinite number of Stokes phenomena. Finally, they showed that Borel resummation can be used to understand phase transitions.

These findings could open up potential applications of resurgence in QFT along with opportunities to explore problems such as hadron dynamics.