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The holographic principle is an intriguing but still-hypothetical paradigm concerning the nature of space, time and the quantum at the most fundamental level. It originates in the enigmatic quantum physics of black holes and efforts to reconcile quantum mechanics with general relativity. The principle posits that quantum spacetime can be understood as the holographic image projected from a quantum hologram (which does not involve gravity) living on the boundary of the spacetime, often at infinity. While this may at first sound impossible, a striking and mathematically precise realization for negatively-curved spacetimes, constructed top-down from string theory, is provided by the so-called Anti-deSitter/Conformal Field Theory (AdS/CFT) correspondence.
This Simons Collaboration seeks to realize the holographic principle in (nearly) flat spacetimes like the one we inhabit. A combination of recent discoveries in disparate fields make this so-far-elusive goal potentially within reach. We use a combined bottom-up and top-down approach and are guided by, but do not assume, results from string theory. This endeavor has come to be known as celestial holography.
Finding a holographic dual pair means constructing the boundary hologram and showing that the projected holographic image is a consistent bulk quantum theory of gravity. The first (bottom-up) step in the construction of any such dual pair is the identification of symmetries which must govern both sides of the pair. Using recent syntheses of old and new results on asymptotic symmetries, soft theorems and the gravitational memory effect, it has been shown that every consistent quantum theory of gravity universally enjoys the conformal symmetries of a two-dimensional CFT living on the celestial sphere at light-like infinity. This ‘celestial CFT’ provides a potential hologram for four-dimensional quantum gravity in asymptotically flat spacetimes. The conformal symmetries are only one entry in an infinite tower of powerful symmetries known as w-infinity which play a central role in Penrose’s solution of twistor theory.
Understanding the universal properties of quantum gravity independent of short-distance microphysics.
One would also like to have a mathematically rigorous top-down construction of a celestial holographic dual pair. Even if simplified or physically unrealistic, it could usefully guide the bottom-up construction of a hologram for the natural world. Fortuitously, there has been a recent explosion of complementary advances in mathematical physics which leverages techniques from algebraic geometry and homological algebra to define quantum structures on twistor space and compute a broad class of both bulk and boundary observables in a variety of models. These independent efforts landed on precisely the same mathematical structures as those sought in the bottom-up approach. The goal of this project is to exploit this synergy and understand holography in asymptotically flat spacetimes along with the concomitant mathematics.
Using twistor theory and rigorous mathematics to construct exact celestial dual pairs.