Heidelberg 2022 – wissenschaftliches Programm

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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 2: Gravity, Amplitudes, AdS/CFT

MP 2.5: Vortrag

Montag, 21. März 2022, 17:55–18:15, MP-H5

Hyperbolic tilings and discrete holography — •Giuseppe Di Giulio — Julius-Maximilians-Universität Würzburg

The AdS/CFT correspondence is one of the most important breakthroughs of the last decades in theoretical physics. A recently proposed way to get insights on various features of this duality is achieved by discretising the Anti-deSitter spacetime. Within this program, we consider the Poincaré disk (fixed time slice of three-dimensional Anti-deSitter spacetime) discretised by introducing a regular hyperbolic tiling on it. This breaks the isometry group of the Poincaré disk down to a discrete subgroup. In a possible discrete version of the AdS/CFT correspondence, such a discrete group is expected to characterise also the quantum theory living on the boundary of the hyperbolic tiling. In this talk, we discuss the properties that such a boundary theory must have. The bulk tessellation we study induces an aperiodic spatial modulation on any model defined on the boundary. This provides an interesting bridge with the aperiodic quantum chains, well-known systems in the literature of condensed matter theory. Furthermore, in view of examining possibilities for establishing a duality in this setup, we investigate the entanglement properties of the tiled bulk (obtained through a discretised version of the Ryu-Takayanagi formula for the holographic entanglement entropy) and of some possible boundary theories.