Aspects of holography

Abstract

In the thesis we studied various aspects of holography principle, especially in the context of real time holography and flat/CFT duality. In the first part, we discussed realtime holography within the embedding space formalism. Based on the previous work on the scalar fields, we presented matching conditions for on-shell integer spin fields when going from Euclidean to Lorentzian signature on AdS background. The main content of the second part is to develop the AdS/CFT correspondence into the flat/CFT correspondence. More precisely, for scalar fields, we constructed the dictionary between flat spacetime and the CFT on the boundary which works the same as AdS/CFT dictionary from the bottom-up point of view. After analysing the behaviour of scalar field modes on hyperbolic slices of Minkowski and performing the holographic renormalisation for the associated onshell action, we obtain a holography dictionary between the bulk theory and the corresponding dual theory on the celestial sphere. We propose that a single scalar field in the bulk is dual to two series of operators on the celestial sphere; the scaling dimension of these operators takes values on the principal series. Moreover, we will see that the two series of operators can be interpreted as ingoing and outgoing waves in the bulk. We illustrate our dictionary with the example of a single shock wave. The third part is basically the extension of construction of the flat/CFT dictionary from scalar fields to gravitational theories. Asymptotically flat spacetime is built up by asymptotically AdS hyperboloid slices in terms of Fefferman Graham coordinates together with soft modes propagating between different slices near the null boundary. Then we construct the flat holography dictionary based on studying Einstein equation at zero and first order and it turns out that these correspond to the description of hard and soft sector for the field theory from the boundary point of view. The explicit expression for energy-stress tensor is also determined by performing holographic renormalisation on the Einstein Hilbert action

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Identifiers

ORCID for Carlos Mafra: orcid.org/0000-0001-9842-9654

ORCID for Marika Taylor: orcid.org/0000-0001-9956-601X

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