Abstract: Holography is one of the most interesting examples of dualities in physics. At the same time, we still do not have a complete understanding of what holography entails, and what the world would look like if holography were true. In this talk, my goal will be to make some progress on these issues, by discussing the formulation of the common core theory for holographic dualities. This addresses both the aforementioned questions about holography, but also deepens our understanding of dualities, by giving an explicit formulation of the common core for holography, arguably one of the hardest cases for this approach. To define this common core theory, I employ the tools of von Neumann algebras, whose relevance for holography has been the subject of much recent work in theoretical physics. Via von Neumann algebras, I am able to describe the common core for holography in the semiclassical limit, and then extend this construction to both the regime where string theoretic effects are significant, and the one where quantum gravitational effects are significant. I also discuss the possibility of using matrix models to address the non-perturbative regime of the theory, where both string theoretic and quantum gravitational effects are significant. Along the way, I highlight a variety of philosophical issues raised by this construction. The first one concerns the way that the common core theory describes the physics of holography in different regimes: in particular, I will suggest that the common core theory relates to the specific physics in a given regime in a way reminiscent to Gelfand duality, i.e. the duality between a topological space and the algebra of functions on it. A consequence of this observation is that, in different regimes, the common core theory will describe different ontologies: for example, in the semiclassical regime, it will have an ontology based on spacetime and quantum fields, not shared by the string theoretic or quantum gravitational regimes. A second point, following from this one, concerns the status of the common core theory: the common core theory provides a cross-regime description, which provides the only structure capable of describing physics in all regimes. In other words, the common core theory is the only theory whose operator algebra covers all regimes where the holographic duality applies. A consequence of this observation is that in holography we have two different, complementary notions of fundamentality: one where what is fundamental is what lives, e.g., at the highest energies, and one where what is fundamental is what is most general, in this case the common core theory. A final point concerns the semiclassical limit in holography and emergence: and in particular, the appearance of a moduli space-like structure in the semiclassical limit of holography, which I analyze using the tools of the recently developed geometric view of theories. This highlights how the geometric view, and related ideas, can be used as organizing principles to make sense of the world described by holography.
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Philosophy of Physics Seminar Convenor: Sam Fletcher | Philosophy of Physics Group Website
