**Branco Weiss Fellow Since**

2021

**Research Category**

Theoretical High Energy Physics

**Research Location**

Stanford University, USA

**Background**

Einstein's theory of general relativity is our most successful description of gravitational physics. It works by identifying the gravitational field with the geometry of spacetime itself. Its many predictions from the perihelion precession of Mercury's orbit to black holes and the gravitational waves generated by their mergers have been confirmed by over a century's observations and experiments.
The issue however is that we lack an understanding of the micro-structure from which the geometry of spacetime emerges. The situation is akin to having an understanding of the laws that govern the flow of fluids without knowing that the fluids themselves are composed of molecules. The most compelling hypothesis about the quantum nature of the gravitational field is known as the Holographic principle. It states that the quantum gravitational physics in some region of space is encoded equivalently by a quantum system inhabiting the boundary of that region. It was originally proposed to explain why the entropy of black holes scale with the area of the event horizon, the surface that bounds it, as opposed to the volume of the black hole's interior. This result was due to Jacob Bekenstein and Stephen Hawking who studied black holes in the presence of quantum fields.
The entropy is a count of the number of microstates of a system, and the scaling of the entropy with the area of the event horizon suggests that the relevant microstates are localized on the event horizon as opposed to being interspersed through the interior of the black hole.
The largest region of interest to us is the observable universe itself. Our observations of supernovae and large-scale structures in our universe indicate that it is expanding at an accelerated rate. Such spaces are modeled in general relativity by a solution to the field equations known as de Sitter spacetime. As such, light from objects at sufficiently large distances from an observer won't ever reach them. In other words, observers in a universe expanding at an accelerated rate are trapped within cosmic horizons, which demarcates the boundary of their causal influence.
Gibbons and Hawking taught us that the entropy of de Sitter space scales with the area of the cosmic horizon, much like in the case of black holes. This tempts us to apply the holographic principle to the region within an observer's cosmic horizon in de Sitter space and understand the physics of the putatively dual quantum system inhabiting the cosmic horizon.

**Details of Research**

The most successful instantiation of the holographic principle is known as the AdS/CFT correspondence. It is a duality between quantum gravity in spaces with negative cosmological constant called Anti de Sitter space (AdS), and a non-gravitational system living on the boundary of AdS space described by a conformal quantum field theory (CFT). Unfortunately, this is a mathematically idealized setting that is too unlike our observable universe. In particular, the universe we live in has positive cosmological constants, and the observable universe is a region of finite spacetime volume unlike AdS space that has infinite volume. Peeling away these idealizations is the focus of Dr. Vasudev Shyam’s research.
In particular, Dr. Shyam starts with the conformal field theories that possess dual descriptions in terms of gravitational physics in AdS space and deform them by a certain set of operators which modify the short distance behaviour of the CFT in such a way that these deformed theories have a dual description in terms of gravity in a finite region of de Sitter space. Specifically, he will study the deformation of the aforementioned conformal field theories by a combination of the so called $T^2$ operator – a composite operator formed from a specific contraction of the energy momentum tensor, and the boundary cosmological constant operator $\Lambda_d$. By tuning the parameter associated to this combined deformation to its extreme value, the deformed quantum field theory inhabits the cosmic horizon itself. Dr. Shyam’s task is to compute quantities of physical interest in the quantum gravity theory in de Sitter space from the lower dimensional dual $T^2+\Lambda_d$ deformed CFT. Some examples of these quantities are the entropy of the cosmic horizon, the rate of particle production in de Sitter space and the radial wavefunction of the de Sitter universe.
This research will combine methods and insights from the theory of general relativity, quantum field theory, quantum information theory, cosmology and the renormalization group. Understanding the deformed conformal field theory inhabiting the cosmic horizon will lead to an understanding of the micro-structure from which the substrate of space itself emerges.