Higher Spin Gravity and Holography

According to a widely-known tale, Newton was inspired to discover a theory of gravity by seeing an apple fall from a tree. His theory had a great success in explaining the rotation of planets around the sun and the behaviour of other massive bodies. Around 200 years later, Einstein perfected Newton gravity. Einstein gravity describes the Universe and the motion of galaxies, and we still use this theory today. However, to reconcile the motion of stars in the galaxy around their galactic centre with Einstein gravity, we need to add dark matter, and Einstein gravity does not tell us what this is. For example an extra massive particle can provide dark matter candidate while modifying gravity. Einstein gravity also requires cosmological constant term to explain accelerated expansion of the Universe. This term, added by hand, describes 70 percent of energy in the Universe. The hope is, that once we know the real quantum theory of gravity, we will understand the origin of dark energy and dark matter. One of the great contenders for such a theory is higher spin gravity. This theory should also explain other constituents in the Universe. We call it higher spin gravity because it must contain graviton and particles of all higher spins to be consistent. Particles are the smallest constituents of the Universe. Graviton, for example, is a particle which is responsible for gravitational waves, which we recently measured, and it has spin 2. That means that it has to turn around itself 1/2 times to look the same as in the beginning. The spin s particle will have to turn around itself 1/s times to look the same again. The rotation, we need to understand in quantum sense, the spin is intrinsic, it is a property of the particle. It is very difficult to constrain this many higher spin particles and there are number of obsta- cles. They refer to constraining interactions with higher spin particles. In 2016 the endeavour to circumvent them was successful using additional symmetries to specify the theory, which led to new consistent higher spin gravity models. New models that I will study here contain: (i) chiral symmetry, which in physics says whether the particle without mass spins in the same direction as the direction in which it moves, and (ii) conformal symmetry. Conformal symmetry says that if we imagine our space as a balloon, the physical laws on the balloon will be the same before and after it has been inflated. An important tool for studying gravity theories is holography. It tells us that information about a gravity theory in d-dimensional space is encoded in the d-1 dimensional boundary of the space. The theory at the boundary is a quantum theory. Quantities in gravity theory have corresponding quantities in the theory at the boundary. Holography allows us to learn about both theories, by looking only from one side. This is the main tool I will use in this project.