November 21: “Fractons gauge theory vs Gravity” by Francisco Peña Benítez

Fractons, exotic quasiparticles found in specific condensed matter systems, showcase intriguing properties, notably limited mobility, challenging conventional notions of particle physics and capturing considerable attention in quantum matter exploration. One category of fracton theories revolves around the conservation of certain abelian charges and a specific quantity of their multipole moments. The most renowned case involves systems preserving dipole moments, which have been demonstrated to be dual to the theory of elastic media in two dimensions. This duality transforms phonon fields into a generalized gauge theory featuring scalar and symmetric tensor fields, while elastic topological defects become fractonic particles minimally coupled to the gauge fields.
Numerous authors have pointed out that these gauge fields show parallels with linearized gravity theory. In this talk, I will introduce the concept of dipole-conserving systems and delve into their spacetime symmetries. Subsequently, I will posit that the associated symmetry algebra can be incorporated into the Poincaré group in one extra dimension, recovering itself following a sequence of pseudo-Carollian-Aristotelian contractions. Furthermore, we propose a non-Einsteinian gravitational gauge theory that, through the algebra contraction, gives rise to a collection of general gauge theories, encompassing some models previously examined in the literature.