Generalized SYK/JT correspondences

According to the holographic principle, the number of dimensions amazingly is a matter of perspective. We can choose to describe the same physical situation using two theories in different dimensions. The higher-dimensional description is a quantum theory with gravity. The lower- dimensional description is a quantum theory without gravity. The best-known implementation of the holographic principle emerged from string theory, known as "Anti-deSitter/Conformal Field Theory" (AdS/CFT) correspondence. The disadvantage of AdS/CFT is that, unlike the Universe we inhabit, it requires a negative cosmological constant. A key long-term goal in theoretical physics is to find out how general the holographic principle is, and if it works in our Universe. In this project, we approach this goal through the lens of lower- dimensional gravity. While conceptually essentially as rich as its higher-dimensional cousins, technically gravity in lower dimensions is much more tractable. This means that some of the puzzles raised by quantum gravity and holography can be addressed with precise calculations. In the past five years, the physics community focused a particular holographic model. It relates a specific model of two-dimensional gravity, the "Jackiw-Teitelboim model" (JT), to a model of randomly interacting particles in one dimension, the "Sachdev-Ye-Kitaev" model" (SYK). Unfortunately, the JT/SYK correspondence still relies on AdS. The main goal of the current project to generalize the JT/SYK correspondence to two-dimensional gravity models that do not necessarily describe AdS. If successful, this sets the stage for novel holographic correspondences beyond the AdS/CFT paradigm.

According to the holographic principle, the number of dimensions is, amazingly, a matter of perspective. We can choose to describe the same physical situation using two theories in different dimensions. The higher-dimensional description is a quantum theory with gravity. The lower-dimensional description is a quantum theory without gravity. The best-known implementation of the holographic principle emerged from string theory, known as "Anti-deSitter/Conformal Field Theory" (AdS/CFT) correspondence. The disadvantage of AdS/CFT is that, unlike the Universe we inhabit, it requires a negative cosmological constant. A key long-term goal in theoretical physics is to find out how general the holographic principle is and if it works in our Universe. In this project, we approached this goal through the lens of lower-dimensional gravity. While conceptually essentially as rich as its higher-dimensional cousins, technically, gravity in lower dimensions is much more tractable. This means that some of the puzzles raised by quantum gravity and holography can be addressed with precise calculations. In the past decade, the physics community focused on a particular holographic model. It relates a specific model of two-dimensional gravity, the "Jackiw-Teitelboim model" (JT), to a model of randomly interacting particles in one dimension, the "Sachdev-Ye-Kitaev" model (SYK). Unfortunately, the JT/SYK correspondence still relies on AdS. The main goal of the current project is to generalize the JT/SYK correspondence to two-dimensional gravity models that do not necessarily describe AdS. If successful, this sets the stage for novel holographic correspondences beyond the AdS/CFT paradigm. In the early stages, the focus shifted quickly to the particular example of flat space holography, since this research field has been developing rapidly during the past five years, leading to numerous novel insights. Our project provides a JT/SYK-like model and addresses aspects of both the gravity side and the field theory side, which turned out to be governed by Carrollian CFTs. During the course of this project, we studied numerous aspects of these field theories. Our most recent discovery was universal sectors of two-dimensional Carrollian CFTs and their flat space holographic interpretation.