Physics Seminar
Date: Wednesday, 9 October 2024
Time: 12:00 PM
Venue: Lecture Hall 6
Constructive Holography
Pratik Roy
University of the Witwatersrand, Johannesburg.
09-10-24

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Abstract

I will describe a construction of the holographic bulk dual of the singlet sector of a free, massless N x N scalar matrix in d-dimensional Minkowski space in the large N limit. This will be based on the formalism of Collective Field Theory, which naturally reorganises the hbar expansion of a field theory as a 1/N expansion. I will start by briefly reviewing this formalism, and the construction of the bulk dual to the O(N) vector model using bilocal collective fields. Moving on to the matrix theory, I will provide an explicit map to AdS_{d+1} from the coordinates of the multilocal collective field excitations of the scalar fields. Remaining multilocal field coordinates will be shown to form a compact internal manifold. The bulk equations of motion (for higher spin bulk fields) will tell us how to pick boundary fields in a specific representation from the collective fields. Using a few simple examples, I will describe how harmonic expansion of bulk fields on the internal manifold leads to specific boundary operators. This constitutes a derivation of the GKPW dictionary for our theory, relating boundary values of bulk fields to CFT operators.

References: 2408.06089, 2406.18248, 2405.04148, 2403.19391, 2307.05032