Can Dirac Fields Source Traversable Wormholes?

Traversable wormholes have captivated the interest of the public and of theoretical physicists since their inception, with a recent resurgence of interest in the context of holography. While wormhole geometries are permissible within the framework of general relativity, they require matter with "negative energy" to sustain them, specifically matter that violates the null energy condition on a sufficiently large scale. Typical classical matter, however, does not possess the necessary properties to support such geometries.

The question has remained open as to whether a Dirac field can generate sufficient violations of the null energy condition to source a traversable wormhole. In this talk, I will present recent progress in exploring this possibility for positive-frequency Dirac fields within static, spherically symmetric wormhole spacetimes. Building on an analytic analysis, I will describe numerical explorations that probe the existence/non-existence of such wormhole solutions. These computations aim to clarify whether solutions to the Dirac equation can provide the "negative energy" needed to make static, spherically symmetric wormholes viable without resorting to introducing nonphysical exotic matter.