Ph.D XXXIX

Supervisor: Daniele Pranzetti, Stefano Ansoldi

Phone: 

Room: Rizzi L2-11-DE

Mail: desimone.gianfranco@spes.uniud.it

Research Project

Higher spin dynamics at finite distance

Symmetries play a pivotal role in the description of physical theories. The most powerful tools we have to characterize the symmetry content of a physical theory are Noether’s theorems, which establish a deep relation between symmetries transformations and conserved charges. In particular, to construct the physical states of a given theory, one has to be careful in distinguishing the ‘real’ symmetries from the trivial ones (gauge), the so-called redundancies. However, the above distinction almost fails in the presence of boundaries, where these redundancies become actually physical. When one deals with boundaries at finite distance, these ‘would-be-gauge’ degrees of freedom are defined on a codimension-2 surface, called the corner, and enter in the definition of the entanglement entropy between the two subregions. The group symmetry is now larger than the previous one, since includes also the surface symmetries. This is a first hint towards an holographic description of the theory.

Perhaps a most striking result occurs for asymptotic boundaries and especially in gravitational theories. A large-r analysis of asymptotically flat spacetimes in 4-dimensions has shown that asymptotic symmetry group is infinite- dimensional, containing the Poincaré group as subgroup. This new symmetry group, the so-called BMS group, acts on an asymptotic sphere of codimension-2, referred to as the celestial sphere.

Consequently, these asymptotic symmetries constraint the gravitational scattering through Ward identities, which turn out to be equivalent to Weinberg’s soft theorems. In light of this, if one considers sub-leading terms in the large-r expansions of the metric, an infinite tower of soft theorems emerges, as a result of the conservation of higher-spin charges. This infinite tower of conserved charges forms an algebra known as the w_1+∞ algebra.

The main goal consists of deriving the aforementioned higher spin charges for boundaries at finite-distance, mainly exploiting the covariant phase space framework and the Newman-Penrose formalism. In particular, our analysis will focus especially on a particular class of null hypersurfaces at finite distance, namely the (future) horizon of a black hole. Therefore, our results will be useful in shedding light on the symmetry content of gravitational theories and also in the context of black hole’s information loss problem (through the soft hair proposal).