Intertwining Operator Realization of Non-Relativistic Holography

TL;DR

This paper provides a group-theoretic framework for non-relativistic holography, explicitly constructing boundary-to-bulk operators and analyzing their properties within representation theory, connecting bulk and boundary fields.

Contribution

It introduces an explicit construction of boundary-to-bulk operators for non-relativistic holography using representation theory, without relying on specific actions, and relates boundary fields with conjugated conformal weights.

Findings

Constructed boundary-to-bulk operators explicitly

Showed boundary and bulk operators are intertwining operators

Reproduced earlier non-relativistic scalar field results

Abstract

We give a group-theoretic interpretation of non-relativistic holography as equivalence between representations of the Schrodinger algebra describing bulk fields and boundary fields. Our main result is the explicit construction of the boundary-to-bulk operators in the framework of representation theory (without specifying any action). Further we show that these operators and the bulk-to-boundary operators are intertwining operators. In analogy to the relativistic case, we show that each bulk field has two boundary fields with conjugated conformal weights. These fields are related by another intertwining operator given by a two-point function on the boundary. Analogously to the relativistic result of Klebanov-Witten we give the conditions when both boundary fields are physical. Finally, we recover in our formalism earlier non-relativistic results for scalar fields by Son and others.