Speaker
Description
\textbf{Abstract:\}
In this talk, the Spin(4) gauge formulation of spacetime with a Cartan khronon field is presented. As motivation, the relation between Euclidean and Lorentzian descriptions is recalled as a Wick-rotation prescription relating two dynamically equivalent descriptions of the same underlying field configurations, once a time direction is selected by the Cartan khronon. Within this setting, the Spin(4) theory provides a gauge-theoretic description of spacetime in which the coframe structure emerges from the covariant derivative of the khronon field.\
The full theory involves both self-dual and anti-self-dual sectors of the Spin(4) connection. A symmetry-breaking pattern is then discussed, in which the distinction between time and space selects a preferred structure and is accompanied by a chiral reduction of the gauge sector. This transition can be viewed as a passage from a Palatini-like Spin(4) phase to a self-dual (Ashtekar-like) formulation, in which only the self-dual sector governs the gravitational dynamics and reproduces the standard general relativistic behavior.\
Within this chiral phase, gravitational instantons provide natural test configurations, as their (anti-)self-dual nature confines them to a single sector of the Spin(4) decomposition, allowing one to probe whether this sector alone reproduces the gravitational dynamics. This perspective is illustrated through the example of the Eguchi–Hanson gravitational instanton, which is presented as a first explicit instanton solution in this framework.\