The holographic dual to general covariance

          @misc{ pirsa_PIRSA:17060024,
            doi = {10.48660/17060024},
            url = {https://pirsa.org/17060024},
            author = {Shyam, Vasudev},
            keywords = {Other},
            language = {en},
            title = {The holographic dual to general covariance},
            publisher = {Perimeter Institute},
            year = {2017},
            month = {jun},
            note = {PIRSA:17060024 see, \url{https://pirsa.org}}
          }
          

Abstract

One of the defining features of holography is the geometerization of the renormalization group scale. This means that when a quantum field theory is holographically dual to a bulk gravity theory, then the direction normal to the boundary in the bulk (the `radial' direction) is to be interpreted as the energy scale of the dual quantum field theory. So this direction can be seen to be `emergent', and the evolution of bulk fields along this direction is equated with the renormalization group flow of sources or couplings of boundary operators. Given that gravitational theories are generally covariant, this emergent direction must be treated on equal footing as those of the space on which the boundary field theory lives. I will describe the precise integrability condition the renormalization group flow need satisfy which encodes this peculiar response of the quantum field theory under coarse graining so as to respect this property of covariance. In other words, this condition is `dual' to general covariance itself.