Intertwining Operator Realization of Non-Relativistic Holography

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.

15 pages, LATEX; Published version

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• Irreducible weight modules over the Schr{ö}dinger Lie algebra in $(n+1)$ dimensional space-time
• Generalized Heisenberg algebra and (non linear) pseudo-bosons
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• Bi-squeezed states arising from pseudo-bosons
• Unitary representations of N-conformal Galilei group
• Appearances of pseudo-bosons from Black-Scholes equation
• A differential operator realisation approach for constructing Casimir operators of non-semisimple Lie algebras
• Galilean conformal algebras in two spatial dimension
• Lowest Weight Representations of Super Schrodinger Algebras in One Dimensional Space
• On Casimir Operators of Conformal Galilei Algebras
• Non self-adjoint Hamiltonians with complex eigenvalues
• Lowest weight representations of super Schrodinger algebras in low dimensional spacetime
• Gibbs states defined by biorthogonal sequences
• Category O for the Schrödinger algebra
• Classification of the Reducible Verma Modules over the Jacobi Algebra ${\mathcal{G}}_2$
• Weyl Anomaly in NonRelativistic CFTs
• The Lie algebra of the lowest transitively differential group of degree three
• Anti de Sitter Holography via Sekiguchi Decomposition
• Invariant differential operators for the Jacobi algebra ${\mathcal{G}}_2$
• Tenfold Way for Holography : AdS/CFT and Beyond