Physics Seminar
Date: Tuesday, 3 December 2024
Time: 11.00 AM
Title: Constructive holography for a single free matrix
Venue: Seminar Hall
Constructive holography for a single free matrix
Pratik Roy
University of the Witwatersrand, Johannesburg.
03-12-24

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Abstract

I will start with a very quick recap of my last talk, describing the construction of the bulk dual to the O(N) vector model using bilocal collective fields. For the theory of a free, massless N x N scalar matrix in d-dimensional Minkowski space in the large N limit, we will make a change of coordinates in field space and coordinate space. These transformations lead to a theory with massless and massive fields of all integer spins in AdS_{d+1}. Extra coordinates in the collective fields will be shown to form compact internal manifolds. 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.