Nested holography
Kostas Filippas
Phys. Rev. D 111, 086018 (2025) - Published 15 April, 2025
Recently, we introduced a symmetry on the structure of angular momentum that interchanges internal and external degrees of freedom. The spin-orbit duality is a holographic map that projects a massive theory in four-dimensional flat spacetime onto the three-dimensional null infinity. This cylinder has radius and, quantum mechanically, its vacuum state is a fuzzy sphere. Progress shows that, first, this duality realizes the Hopf map, a fact manifest on the superparticle. Second, the bulk Poincarè group transforms into the conformal group on the cylinder. In fact, the general version of the duality yields that the dual symmetries include the Bondi-Metzner-Sachs group, as is appropriate at null infinity. As an example, the Landau levels in are shown to match those of a Dirac monopole on the dual , in the thermodynamic limit. This dual system is actually identified with a three-dimensional critical Ising model. The map is then realized on massive fermions in flat space which, indeed, are the hologram of massless fermions on the cylinder. However, the dual space is really the conformal class of , naturally enclosing the universal cover of a conformally compactified four-dimensional anti–de Sitter () spacetime. We argue that, in the absence of interactions, the massless fermions on the conformal boundary are, in turn, dual to massive fermions in . For free fermions, all path integrals—the ones in and and —are shown to match. Hence, AdS/CFT duality emerges into a larger context, where one holography nests inside the other, suggesting a complete holographic bridge between fields in flat space and the AdS superstring.
